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<span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Must be worked on (anyone know what the "special rules" are ?): subsection</span> </button> <ul id="toc-Must_be_worked_on_(anyone_know_what_the_"special_rules"_are_?):-sublist" class="vector-toc-list"> <li id="toc-Table_method_(for_quadratics)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Table_method_(for_quadratics)"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Table method (for quadratics)</span> </div> </a> <ul id="toc-Table_method_(for_quadratics)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Sum/difference_of_two_cubes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sum/difference_of_two_cubes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Sum/difference of two cubes</span> </div> </a> <span 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class="ext-discussiontools-init-sidebar-meta">4 comments</span> <ul id="toc-Difference_of_two_cubes,forth_powers,fifth_powers,etc.-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ratio_Method_for_factoring_quadratics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ratio_Method_for_factoring_quadratics"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Ratio Method for factoring quadratics</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-Ratio_Method_for_factoring_quadratics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cleanup_needed" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cleanup_needed"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Cleanup needed</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-Cleanup_needed-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cubed_polynomials_plus_7_imaginary" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cubed_polynomials_plus_7_imaginary"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Cubed polynomials plus 7 imaginary</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-Cubed_polynomials_plus_7_imaginary-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Error_in_"other_common_formulas"" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Error_in_"other_common_formulas""> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Error in "other common formulas"</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">2 comments</span> <ul id="toc-Error_in_"other_common_formulas"-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Factoring_by_grouping" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Factoring_by_grouping"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Factoring by grouping</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-Factoring_by_grouping-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Last_link_in_the_external_links_section" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Last_link_in_the_external_links_section"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Last link in the external links section</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">2 comments</span> <ul id="toc-Last_link_in_the_external_links_section-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Funny_introduction_to_the_article" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Funny_introduction_to_the_article"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Funny introduction to the article</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">2 comments</span> <ul id="toc-Funny_introduction_to_the_article-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-I_think_this_page_requires_clean-up_and/or_attention" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#I_think_this_page_requires_clean-up_and/or_attention"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>I think this page requires clean-up and/or attention</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-I_think_this_page_requires_clean-up_and/or_attention-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Discuss_the_usage_difference_between_"factor"_and_"factorization"" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Discuss_the_usage_difference_between_"factor"_and_"factorization""> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>Discuss the usage difference between "factor" and "factorization"</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">2 comments</span> <ul id="toc-Discuss_the_usage_difference_between_"factor"_and_"factorization"-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Does_Factorization_serve_a_practical_purpose?" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Does_Factorization_serve_a_practical_purpose?"> <div class="vector-toc-text"> <span class="vector-toc-numb">16</span> <span>Does Factorization serve a practical purpose?</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">3 comments</span> <ul id="toc-Does_Factorization_serve_a_practical_purpose?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-LaTeX_Code?" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#LaTeX_Code?"> <div class="vector-toc-text"> <span class="vector-toc-numb">17</span> <span>LaTeX Code?</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-LaTeX_Code?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Refactoring_and_adding_references" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Refactoring_and_adding_references"> <div class="vector-toc-text"> <span class="vector-toc-numb">18</span> <span>Refactoring and adding references</span> </div> 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class="ext-discussiontools-init-sidebar-meta">2 comments</span> <ul id="toc-Error-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Add_Factorisation_by_inspection_section_to_polynomial_section" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Add_Factorisation_by_inspection_section_to_polynomial_section"> <div class="vector-toc-text"> <span class="vector-toc-numb">23</span> <span>Add Factorisation by inspection section to polynomial section</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">4 comments</span> <ul id="toc-Add_Factorisation_by_inspection_section_to_polynomial_section-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" 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screen{html.skin-theme-clientpref-night .mw-parser-output .wpb-category-box{background-color:#0a0a0a}html.skin-theme-clientpref-night .mw-parser-output .wpbs .wpb .wpb-main,html.skin-theme-clientpref-night .mw-parser-output .wpbs .wpb-header{background-color:#302f2d}html.skin-theme-clientpref-night .mw-parser-output .wpbs .banner-shell-inner{background-color:#2e2505}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .wpb-category-box{background-color:#0a0a0a}html.skin-theme-clientpref-os .mw-parser-output .wpbs .wpb .wpb-main,html.skin-theme-clientpref-os .mw-parser-output .wpbs .wpb-header{background-color:#302f2d}html.skin-theme-clientpref-os .mw-parser-output .wpbs .banner-shell-inner{background-color:#2e2505}}</style><table class="tmbox tmbox-notice mw-collapsible innercollapse wpb wpb-table"><tbody><tr class="wpb-header"><td class="wpb-header-icon"><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics-p.svg" class="mw-file-description"><img alt="WikiProject icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/25px-Nuvola_apps_edu_mathematics-p.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/38px-Nuvola_apps_edu_mathematics-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/50px-Nuvola_apps_edu_mathematics-p.svg.png 2x" data-file-width="128" data-file-height="128"/></a></span></td><td class="wpb-header-combined"><a href="/wiki/Wikipedia:WikiProject_Mathematics" title="Wikipedia:WikiProject Mathematics">Mathematics</a> <span class="wpb-header-bubbles import-mid">Mid‑priority</span></td></tr><tr><td class="mbox-text wpb-main" colspan="2"><table><tbody><tr><td class="mbox-image wpb-image"><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics-p.svg" class="mw-file-description"><img alt="WikiProject icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/60px-Nuvola_apps_edu_mathematics-p.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/90px-Nuvola_apps_edu_mathematics-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/120px-Nuvola_apps_edu_mathematics-p.svg.png 2x" data-file-width="128" data-file-height="128"/></a></span></td><td class="mbox-text"><style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128"/></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></span></li></ul>This article is within the scope of <b><a href="/wiki/Wikipedia:WikiProject_Mathematics" title="Wikipedia:WikiProject Mathematics">WikiProject Mathematics</a></b>, a collaborative effort to improve the coverage of <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> on Wikipedia. If you would like to participate, please visit the project page, where you can join <a href="/wiki/Wikipedia_talk:WikiProject_Mathematics" title="Wikipedia talk:WikiProject Mathematics">the discussion</a> and see a list of open tasks.<span class="metadata wpb-metadata"><span class="wpb-project">Mathematics</span><span class="wpb-project_link">Wikipedia:WikiProject Mathematics</span><span class="wpb-banner_name">Template:WikiProject Mathematics</span><span class="wpb-assessment_cat">mathematics articles</span></span></td><td class="mbox-empty-cell"></td></tr><tr><td class="assess import-mid"><a href="/wiki/Category:Mid-priority_mathematics_articles" title="Category:Mid-priority mathematics articles">Mid</a></td><td class="mbox-text" colspan="2">This article has been rated as <b>Mid-priority</b> on the <a href="/wiki/Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Assessment#Priority_scale" class="mw-redirect" title="Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Assessment">project's priority scale</a>.</td></tr></tbody></table></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237879475"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1256394742"><table class="tmbox tmbox-notice mw-collapsible innercollapse wpb wpb-table"><tbody><tr class="wpb-header"><td class="wpb-header-icon"><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="WikiProject icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/25px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/38px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/50px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128"/></a></span></td><td class="wpb-header-combined"><a href="/wiki/Wikipedia:WikiProject_Numbers" title="Wikipedia:WikiProject Numbers">Numbers</a> </td></tr><tr><td class="mbox-text wpb-main" colspan="2"><table><tbody><tr><td class="mbox-image wpb-image"><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="WikiProject icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/80px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/120px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/160px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128"/></a></span></td><td class="mbox-text">This article is within the scope of <b><a href="/wiki/Wikipedia:WikiProject_Numbers" title="Wikipedia:WikiProject Numbers">WikiProject Numbers</a></b>, a collaborative effort to improve the coverage of <a href="/wiki/Number" title="Number">Numbers</a> on Wikipedia. If you would like to participate, please visit the project page, where you can join <a href="/wiki/Wikipedia_talk:WikiProject_Numbers" title="Wikipedia talk:WikiProject Numbers">the discussion</a> and see a list of open tasks.<span class="metadata wpb-metadata"><span class="wpb-project">Numbers</span><span class="wpb-project_link">Wikipedia:WikiProject Numbers</span><span class="wpb-banner_name">Template:WikiProject Numbers</span><span class="wpb-assessment_cat">Numbers articles</span></span></td><td class="mbox-empty-cell"></td></tr><tr><td class="assess import-unknown"><a href="/wiki/Category:Unknown-importance_Numbers_articles" title="Category:Unknown-importance Numbers articles">???</a></td><td class="mbox-text" colspan="2">This article has not yet received a rating on the <a href="/wiki/Wikipedia:WikiProject_Numbers/Assessment#Importance_scale" title="Wikipedia:WikiProject Numbers/Assessment">project's importance scale</a>.</td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table> <meta property="mw:PageProp/toc"/> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Factoring_'"`UNIQ--postMath-00000001-QINU`"'" data-mw-thread-id="h-Factoring_'"`UNIQ--postMath-00000001-QINU`"'-2011-07-05T03:35:00.000Z"><span id="Factoring_.7F.27.22.60UNIQ--postMath-00000001-QINU.60.22.27.7F"></span><span data-mw-comment-start="" id="h-Factoring_'"`UNIQ--postMath-00000001-QINU`"'-2011-07-05T03:35:00.000Z"></span>Factoring <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2}-2b^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}-2b^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee698eec34e6846ad65396ca0b6cf72c597d31a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:8.339ex; height:2.843ex;" alt="{\displaystyle a^{2}-2b^{2}}"/></span><span data-mw-comment-end="h-Factoring_'"`UNIQ--postMath-00000001-QINU`"'-2011-07-05T03:35:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=1" title="Edit section: Factoring '"`UNIQ--postMath-00000001-QINU`"'"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-GabKBel-2011-07-05T03:35:00.000Z-Factoring_'"`UNIQ--postMath-00000001-QINU`"'"></span>In my opinion, this section is a special case of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2}-b^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}-b^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d889199ccf9e44b772541baebe35e97744002f2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.176ex; height:2.843ex;" alt="{\displaystyle a^{2}-b^{2}}"/></span> being <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2}-2b^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}-2b^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee698eec34e6846ad65396ca0b6cf72c597d31a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:8.339ex; height:2.843ex;" alt="{\displaystyle a^{2}-2b^{2}}"/></span>, which yields <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (a-{\sqrt {2}}b)(a+{\sqrt {2}}b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mi>b</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a-{\sqrt {2}}b)(a+{\sqrt {2}}b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bbd49cefe710b2dd912723a0a01482195d60a66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.951ex; height:3.176ex;" alt="{\displaystyle (a-{\sqrt {2}}b)(a+{\sqrt {2}}b)}"/></span> for one, and there is no way of doing this without radicals (assuming <b>a</b> and <b>b</b> are integers) like the editor asks for. Furthermore, it is stated as if the editor wanted help in his homework, but of course without knowing the editor, I will not pass judgement on his intentions, just that it sounds terrible in the article. In any case, unless the section is relevant, which does not seem so, it should be deleted, or at least until what is proposed is found. </p><p>--<a href="/wiki/User:GabKBel" title="User:GabKBel">GabKBel</a> (<a href="/wiki/User_talk:GabKBel" title="User talk:GabKBel">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-GabKBel-2011-07-05T03:35:00.000Z-Factoring_'"`UNIQ--postMath-00000001-QINU`"'" class="ext-discussiontools-init-timestamplink">03:35, 5 July 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-GabKBel-2011-07-05T03:35:00.000Z-Factoring_'"`UNIQ--postMath-00000001-QINU`"'"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-GabKBel-2011-07-05T03:35:00.000Z-Factoring_'"`UNIQ--postMath-00000001-QINU`"'"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Old_comments" data-mw-thread-id="h-Old_comments"><span data-mw-comment-start="" id="h-Old_comments"></span>Old comments<span data-mw-comment-end="h-Old_comments"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=2" title="Edit section: Old comments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Whoa! Language alert! </p> <dl><dd>15 factors into primes (verb)</dd> <dd>x2 - 4 factorises (verb)</dd> <dd>In mathematics, factorization (noun)</dd> <dd>The aim of factoring (noun)</dd></dl> <p>Is there a good reason why there are two flavours of each? -- <a href="/wiki/User:Tarquin" title="User:Tarquin">Tarquin</a> 21:25 Sep 22, 2002 (UTC) </p><p><br/> Unfortunately, both <i>factor</i> and <i>factorize</i> are used as synonymous verbs, each being more common in a different context, and each having its own noun form. When discussing the problem of breaking down <i>large</i> numbers, "factorize" is almost always used. In all other contexts it's usually "factor". I prefer the latter because it's shorter, but use the former when talking about the problem for large integers. </p><p>There's also the difference between using an "s" or a "z". That's purely a British vs. American issue, so it would be fine to standardize one way or the other on a given page. </p><p>I think there is a fast method of factoring integer into primes, but it requires a quantum computer. </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Must_be_worked_on_(anyone_know_what_the_"special_rules"_are_?):" data-mw-thread-id="h-Must_be_worked_on_(anyone_know_what_the_"special_rules"_are_?):-2011-01-11T15:51:00.000Z"><span id="Must_be_worked_on_.28anyone_know_what_the_.22special_rules.22_are_.3F.29:"></span><span data-mw-comment-start="" id="h-Must_be_worked_on_(anyone_know_what_the_"special_rules"_are_?):-2011-01-11T15:51:00.000Z"></span>Must be worked on (anyone know what the "special rules" are ?):<span data-mw-comment-end="h-Must_be_worked_on_(anyone_know_what_the_"special_rules"_are_?):-2011-01-11T15:51:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=3" title="Edit section: Must be worked on (anyone know what the "special rules" are ?):"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <div class="mw-heading mw-heading3"><h3 id="Table_method_(for_quadratics)" data-mw-thread-id="h-Table_method_(for_quadratics)-Must_be_worked_on_(anyone_know_what_the_"special_rules"_are_?):-2011-01-11T15:51:00.000Z"><span id="Table_method_.28for_quadratics.29"></span><span data-mw-comment-start="" id="h-Table_method_(for_quadratics)-Must_be_worked_on_(anyone_know_what_the_"special_rules"_are_?):-2011-01-11T15:51:00.000Z"></span>Table method (for quadratics)<span data-mw-comment-end="h-Table_method_(for_quadratics)-Must_be_worked_on_(anyone_know_what_the_"special_rules"_are_?):-2011-01-11T15:51:00.000Z"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=4" title="Edit section: Table method (for quadratics)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span data-mw-comment-start="" id="c-150.176.192.118-2011-01-11T15:51:00.000Z-Table_method_(for_quadratics)"></span>A less used (hard to teach, easy to learn) method often involves creating a multiplication table. </p><p>For example, let's work with 6<i>x</i><sup>2</sup> - 17<i>x</i> + 12. </p><p>Multiply first and last terms. (72<i>x</i><sup>2</sup>) </p><p>What multiplies into 72 (first term) and adds up to -17(<i>x</i>) (middle term)? </p><p>-9 and -8 </p><p>In the table, place the first term in the first box and the last in the last box. Fit the (in this example) -9 and -8 in the remaining boxes. Find the <a href="/wiki/Greatest_common_factor" class="mw-redirect" title="Greatest common factor">GCF</a> up and down and side to side for each row for the answer. </p> <table class="wikitable"> <tbody><tr> <td>6<i>x</i><sup>2</sup></td> <td>-8<i>x</i> </td></tr> <tr> <td>-9<i>x</i></td> <td>12 </td></tr></tbody></table> <p>The answer would be (3<i>x</i>-4)(2<i>x</i>-3) </p><p>This method is very decisive and much faster than the others. However, there are a few special rules surrounding the method, but when all of the rules are followed, it works every time. </p> <dl><dd>I am not sure this method is faster than the generalized AC method shown. In this example ac = 72. Examination of the factors of 72 gives -9 -8 = -17 = b, as above. From here we get:</dd></dl> <dl><dd>6<i>x</i><sup>2</sup> - 17<i>x</i> + 12 = (6<i>x</i> - 8)(6<i>x</i> - 9)/6 = (2)(3<i>x</i> - 4)(3)(2<i>x</i> - 3)/6 = (3<i>x</i> - 4)(2<i>x</i> - 3). <span style="font-size: smaller;" class="autosigned">—Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/150.176.192.118" title="Special:Contributions/150.176.192.118">150.176.192.118</a> (<a href="/wiki/User_talk:150.176.192.118" title="User talk:150.176.192.118">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-150.176.192.118-2011-01-11T15:51:00.000Z-Table_method_(for_quadratics)" class="ext-discussiontools-init-timestamplink">15:51, 11 January 2011 (UTC)</a><span data-mw-comment-end="c-150.176.192.118-2011-01-11T15:51:00.000Z-Table_method_(for_quadratics)"></span></span><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-150.176.192.118-2011-01-11T15:51:00.000Z-Table_method_(for_quadratics)"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Sum/difference_of_two_cubes" data-mw-thread-id="h-Sum/difference_of_two_cubes-2006-04-15T21:10:00.000Z"><span id="Sum.2Fdifference_of_two_cubes"></span><span data-mw-comment-start="" id="h-Sum/difference_of_two_cubes-2006-04-15T21:10:00.000Z"></span>Sum/difference of two cubes<span data-mw-comment-end="h-Sum/difference_of_two_cubes-2006-04-15T21:10:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=5" title="Edit section: Sum/difference of two cubes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-RussellMcKenzie-2006-04-15T21:10:00.000Z-Sum/difference_of_two_cubes"></span>I'm here to learn, but shouldn't the factorization be (x-10)(x^2+10x+100) to expand to (x^3 - 1000)? <a href="/wiki/User:RussellMcKenzie" title="User:RussellMcKenzie">Sparky</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-RussellMcKenzie-2006-04-15T21:10:00.000Z-Sum/difference_of_two_cubes" class="ext-discussiontools-init-timestamplink">21:10, 15 April 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-RussellMcKenzie-2006-04-15T21:10:00.000Z-Sum/difference_of_two_cubes"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-RussellMcKenzie-2006-04-15T21:10:00.000Z-Sum/difference_of_two_cubes"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Mets501-2006-04-15T21:31:00.000Z-RussellMcKenzie-2006-04-15T21:10:00.000Z"></span>You're so right. My apologies! --<a href="/wiki/User:Mets501" title="User:Mets501"><i>Mets501</i></a><a href="/wiki/User_talk:Mets501" title="User talk:Mets501"><sup>talk</sup></a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Mets501-2006-04-15T21:31:00.000Z-RussellMcKenzie-2006-04-15T21:10:00.000Z" class="ext-discussiontools-init-timestamplink">21:31, 15 April 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Mets501-2006-04-15T21:31:00.000Z-RussellMcKenzie-2006-04-15T21:10:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Mets501-2006-04-15T21:31:00.000Z-RussellMcKenzie-2006-04-15T21:10:00.000Z"></span></dd> <dd><span data-mw-comment-start="" id="c-RussellMcKenzie-2006-04-15T22:44:00.000Z-RussellMcKenzie-2006-04-15T21:10:00.000Z"></span>Haha no problem! Keep up the good work. <a href="/wiki/User:RussellMcKenzie" title="User:RussellMcKenzie">Sparky</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-RussellMcKenzie-2006-04-15T22:44:00.000Z-RussellMcKenzie-2006-04-15T21:10:00.000Z" class="ext-discussiontools-init-timestamplink">22:44, 15 April 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-RussellMcKenzie-2006-04-15T22:44:00.000Z-RussellMcKenzie-2006-04-15T21:10:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-RussellMcKenzie-2006-04-15T22:44:00.000Z-RussellMcKenzie-2006-04-15T21:10:00.000Z"></span></dd></dl> <p><span data-mw-comment-start="" id="c-Mets501-2006-05-28T15:14:00.000Z-Sum/difference_of_two_cubes"></span>Also here is a problem: x^2-y^2+8y+4x-12 should I Factori "x^2-y^2" or "y^2+8y-12"first? </p><p>Factor it to </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+4x+4-(y^{2}-8y+16)=12+4-16}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <mi>x</mi> <mo>+</mo> <mn>4</mn> <mo>−</mo> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>8</mn> <mi>y</mi> <mo>+</mo> <mn>16</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>12</mn> <mo>+</mo> <mn>4</mn> <mo>−</mo> <mn>16</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+4x+4-(y^{2}-8y+16)=12+4-16}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/485a02464948c6297da6a4f2304bba7c81304933" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.499ex; height:3.176ex;" alt="{\displaystyle x^{2}+4x+4-(y^{2}-8y+16)=12+4-16}"/></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x+2)^{2}-(y-4)^{2}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mn>2</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <mn>4</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x+2)^{2}-(y-4)^{2}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/432ca3f2832b283e6c8daaf64357bd9aa5120834" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.319ex; height:3.176ex;" alt="{\displaystyle (x+2)^{2}-(y-4)^{2}=0}"/></span></dd></dl> <p>—<b><a href="/wiki/User:Mets501" title="User:Mets501">M</a><a href="/wiki/User:Mets501/Esperanza" class="mw-redirect" title="User:Mets501/Esperanza"><span style="color:green;"><i>e</i></span></a><a href="/wiki/User:Mets501" title="User:Mets501">ts501</a></b><small><sup><a href="/wiki/User_talk:Mets501" title="User talk:Mets501"><span style="cursor:help;">talk</span></a></sup></small> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Mets501-2006-05-28T15:14:00.000Z-Sum/difference_of_two_cubes" class="ext-discussiontools-init-timestamplink">15:14, 28 May 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Mets501-2006-05-28T15:14:00.000Z-Sum/difference_of_two_cubes"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Mets501-2006-05-28T15:14:00.000Z-Sum/difference_of_two_cubes"></span> </p> <dl><dd><dl><dd><span data-mw-comment-start="" id="c-150.176.192.118-2011-01-11T16:00:00.000Z-Mets501-2006-05-28T15:14:00.000Z"></span>I am not sure where the equal sign comes from. This is also a difference of squares, so the final form is given as:</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x+2+y-4)(x+2-y+4)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mi>y</mi> <mo>−</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mo>−</mo> <mi>y</mi> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x+2+y-4)(x+2-y+4)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/869f2606a786b5ab1e06051259f81fc4cfe3c674" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.281ex; height:2.843ex;" alt="{\displaystyle (x+2+y-4)(x+2-y+4)}"/></span> which simplifies to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x+y-2)(x-y+6)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> <mo>+</mo> <mn>6</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x+y-2)(x-y+6)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d399def1bdd3df394df39b15c8ab20df340094d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.275ex; height:2.843ex;" alt="{\displaystyle (x+y-2)(x-y+6)}"/></span> <span style="font-size: smaller;" class="autosigned">—Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/150.176.192.118" title="Special:Contributions/150.176.192.118">150.176.192.118</a> (<a href="/wiki/User_talk:150.176.192.118" title="User talk:150.176.192.118">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-150.176.192.118-2011-01-11T16:00:00.000Z-Mets501-2006-05-28T15:14:00.000Z" class="ext-discussiontools-init-timestamplink">16:00, 11 January 2011 (UTC)</a><span data-mw-comment-end="c-150.176.192.118-2011-01-11T16:00:00.000Z-Mets501-2006-05-28T15:14:00.000Z"></span></span><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-150.176.192.118-2011-01-11T16:00:00.000Z-Mets501-2006-05-28T15:14:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span></dd></dl></dd></dl> <p>FYI, I'm finding the description here very confusing. I've reread it several times. Is there a typo in the description of a^n - b^n and a^n + b^n - maybe left out an "even" in the wording? Anyway, the description is confusing. </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Order_of_sections" data-mw-thread-id="h-Order_of_sections-2006-08-07T16:56:00.000Z"><span data-mw-comment-start="" id="h-Order_of_sections-2006-08-07T16:56:00.000Z"></span>Order of sections<span data-mw-comment-end="h-Order_of_sections-2006-08-07T16:56:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=6" title="Edit section: Order of sections"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-JPD-2006-08-07T16:56:00.000Z-Order_of_sections"></span>I would have expected that the prime factorisation of integers would be before factorisation of polynomials, etc. <a href="/wiki/User:JPD" title="User:JPD">JPD</a> (<a href="/wiki/User_talk:JPD" title="User talk:JPD">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-JPD-2006-08-07T16:56:00.000Z-Order_of_sections" class="ext-discussiontools-init-timestamplink">16:56, 7 August 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-JPD-2006-08-07T16:56:00.000Z-Order_of_sections"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-JPD-2006-08-07T16:56:00.000Z-Order_of_sections"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Mets501-2006-08-07T19:00:00.000Z-JPD-2006-08-07T16:56:00.000Z"></span>Yes, you're right; that would be more logical. I've changed it. —<span style="font: small-caps 14px times; color: red;"><a href="/wiki/User:Mets501" title="User:Mets501">Mets<small>501</small></a> (<a href="/wiki/User_talk:Mets501" title="User talk:Mets501">talk</a>)</span> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Mets501-2006-08-07T19:00:00.000Z-JPD-2006-08-07T16:56:00.000Z" class="ext-discussiontools-init-timestamplink">19:00, 7 August 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Mets501-2006-08-07T19:00:00.000Z-JPD-2006-08-07T16:56:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Mets501-2006-08-07T19:00:00.000Z-JPD-2006-08-07T16:56:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Difference_of_two_cubes,forth_powers,fifth_powers,etc." data-mw-thread-id="h-Difference_of_two_cubes,forth_powers,fifth_powers,etc.-2006-08-28T07:15:00.000Z"><span id="Difference_of_two_cubes.2Cforth_powers.2Cfifth_powers.2Cetc."></span><span data-mw-comment-start="" id="h-Difference_of_two_cubes,forth_powers,fifth_powers,etc.-2006-08-28T07:15:00.000Z"></span>Difference of two cubes,forth powers,fifth powers,etc.<span data-mw-comment-end="h-Difference_of_two_cubes,forth_powers,fifth_powers,etc.-2006-08-28T07:15:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=7" title="Edit section: Difference of two cubes,forth powers,fifth powers,etc."><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Bhowmickr-2006-08-28T07:15:00.000Z-Difference_of_two_cubes,forth_powers,fifth_powers,etc."></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{n}-b^{n}=c^{2}-d^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{n}-b^{n}=c^{2}-d^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d65338d4c0bbd08e395d24f8386b679d93c34b78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:17.777ex; height:2.843ex;" alt="{\displaystyle a^{n}-b^{n}=c^{2}-d^{2}}"/></span> like <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 7^{3}-4^{3}=48^{2}-45^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <msup> <mn>48</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mn>45</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 7^{3}-4^{3}=48^{2}-45^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8694f323bbb754adee997b8d2ac07615fd3a13fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:19.971ex; height:2.843ex;" alt="{\displaystyle 7^{3}-4^{3}=48^{2}-45^{2}}"/></span> <a href="/wiki/User:Bhowmickr" title="User:Bhowmickr">Bhowmickr</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Bhowmickr-2006-08-28T07:15:00.000Z-Difference_of_two_cubes,forth_powers,fifth_powers,etc." class="ext-discussiontools-init-timestamplink">07:15, 28 August 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Bhowmickr-2006-08-28T07:15:00.000Z-Difference_of_two_cubes,forth_powers,fifth_powers,etc."><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Bhowmickr-2006-08-28T07:15:00.000Z-Difference_of_two_cubes,forth_powers,fifth_powers,etc."></span> </p> <dl><dd><span data-mw-comment-start="" id="c-JoergenB-2007-11-01T12:55:00.000Z-Bhowmickr-2006-08-28T07:15:00.000Z"></span>Not very exciting, since <i>any</i> odd integer may be expressed as a difference <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c^{2}-d^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c^{2}-d^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2ef0c7ceae8d1fbab75a91f9bda67a5f45a2102" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.174ex; height:2.843ex;" alt="{\displaystyle c^{2}-d^{2}}"/></span>, with both <i>c</i> and <i>d</i> being integers. <a href="/wiki/User:JoergenB" title="User:JoergenB">JoergenB</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-JoergenB-2007-11-01T12:55:00.000Z-Bhowmickr-2006-08-28T07:15:00.000Z" class="ext-discussiontools-init-timestamplink">12:55, 1 November 2007 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-JoergenB-2007-11-01T12:55:00.000Z-Bhowmickr-2006-08-28T07:15:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-JoergenB-2007-11-01T12:55:00.000Z-Bhowmickr-2006-08-28T07:15:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-150.176.192.118-2011-01-11T16:07:00.000Z-JoergenB-2007-11-01T12:55:00.000Z"></span>How does one express an integer of the form 4n+1 as a difference of squares of integers? that said, the difference in the original problem must either be 0 or -1 mod 4. <span style="font-size: smaller;" class="autosigned">—Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/150.176.192.118" title="Special:Contributions/150.176.192.118">150.176.192.118</a> (<a href="/wiki/User_talk:150.176.192.118" title="User talk:150.176.192.118">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-150.176.192.118-2011-01-11T16:07:00.000Z-JoergenB-2007-11-01T12:55:00.000Z" class="ext-discussiontools-init-timestamplink">16:07, 11 January 2011 (UTC)</a></span><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-150.176.192.118-2011-01-11T16:07:00.000Z-JoergenB-2007-11-01T12:55:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-150.176.192.118-2011-01-11T16:07:00.000Z-JoergenB-2007-11-01T12:55:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-EmilJ-2011-01-11T16:17:00.000Z-150.176.192.118-2011-01-11T16:07:00.000Z"></span>If <i>a</i> = 2<i>n</i> + 1, then <i>a</i> = (<i>n</i> + 1)<sup>2</sup> − <i>n</i><sup>2</sup>.—<a href="/wiki/User:EmilJ" title="User:EmilJ">Emil</a> <a href="/wiki/User_talk:EmilJ" title="User talk:EmilJ">J.</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-EmilJ-2011-01-11T16:17:00.000Z-150.176.192.118-2011-01-11T16:07:00.000Z" class="ext-discussiontools-init-timestamplink">16:17, 11 January 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-EmilJ-2011-01-11T16:17:00.000Z-150.176.192.118-2011-01-11T16:07:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-EmilJ-2011-01-11T16:17:00.000Z-150.176.192.118-2011-01-11T16:07:00.000Z"></span></dd></dl></dd></dl></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Ratio_Method_for_factoring_quadratics" data-mw-thread-id="h-Ratio_Method_for_factoring_quadratics-2006-11-04T20:49:00.000Z"><span data-mw-comment-start="" id="h-Ratio_Method_for_factoring_quadratics-2006-11-04T20:49:00.000Z"></span>Ratio Method for factoring quadratics<span data-mw-comment-end="h-Ratio_Method_for_factoring_quadratics-2006-11-04T20:49:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=8" title="Edit section: Ratio Method for factoring quadratics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Jmatt1122-2006-11-04T20:49:00.000Z-Ratio_Method_for_factoring_quadratics"></span>A teacher at my schoool came up with this method. I like it. </p><p>You multiply (A)(C). Use B. Find two numbers that multiply to give AC, and add to give B. Let's say they are Z and Y </p><p>Now make two columns on paper...each with a ratio. A will be the first number in both ratios. Z will be the second number in the first ratio, and Y will be the second number in the second ratio. </p><p>Reduce if possible. Say you end up with A:Z and A:Y. the answer will be (a+z)(a+y). </p><p>This is what they teach in grade 10. and it's easier/more convenient than the methods described here. <span style="border: 1px solid #000000;"><a href="/wiki/User:Jmatt1122" title="User:Jmatt1122"><i><b><span style="background: #000000; color:#FFFFFF;"> jmatt1122 </span></b></i></a> <b><a href="/wiki/Wikipedia:Counter-Vandalism_Unit" title="Wikipedia:Counter-Vandalism Unit"><span style="color:#b34040;">C</span><span style="color:#66b38c;">V</span><span style="color:#408cb3;">U</span></a><a href="/wiki/User_talk:Jmatt1122" title="User talk:Jmatt1122"><span style="background:#FFFFFF; color:#003333;"> <sup>(Talk)</sup> </span></a></b></span> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Jmatt1122-2006-11-04T20:49:00.000Z-Ratio_Method_for_factoring_quadratics" class="ext-discussiontools-init-timestamplink">20:49, 4 November 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Jmatt1122-2006-11-04T20:49:00.000Z-Ratio_Method_for_factoring_quadratics"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Jmatt1122-2006-11-04T20:49:00.000Z-Ratio_Method_for_factoring_quadratics"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Cleanup_needed" data-mw-thread-id="h-Cleanup_needed-2007-01-05T22:08:00.000Z"><span data-mw-comment-start="" id="h-Cleanup_needed-2007-01-05T22:08:00.000Z"></span>Cleanup needed<span data-mw-comment-end="h-Cleanup_needed-2007-01-05T22:08:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=9" title="Edit section: Cleanup needed"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-MFH-2007-01-05T22:08:00.000Z-Cleanup_needed"></span>The article starts in a nice manner: integers, polynomials and matrices are considered. Sections 1 & 2 still seem to preserve this. </p><p>Then, it goes in a quite wild way: Sections 3 - 6 are somehow "unclassified". Then, section 7 pops up with logics, and matrices are present only in the "see also" section. </p><p>Who has ideas to re-equilibrate this a little? </p><p>As a first suggestion, could one make a 1- or 2-line summary for each of sect. 3-6 into the corresponding chapter (sect.1 or 2), make sect.3 on matrices (or sect.3 : logics (since a little bit related to polynomial factoring), then sect.4: short summary on most important matrix decompositions). </p><p>I suggest to put details from sect.3-6 on (a) separate page(s). </p><p>Another idea would be a subsection of 2 with a title going somehow like "deterministic formulae and/or algorithms for speical cases". </p><p>(So one could know more easily what section would be useful for a given problem, e.g.) </p><p>Or, third idea, make some short sections at the beginning on "what the main body of this article not really is about: integer, matrix & logic factorization" with appropriate links, and then elaborate on the polynomial factoring methods (say, in increasing degree of the polynomials or some other order). </p><p>This is meant as a brainstorming - I'm missing better ideas, so please help. — <a href="/wiki/User:MFH" title="User:MFH">MFH</a>:<a href="/wiki/User_talk:MFH" title="User talk:MFH">Talk</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-MFH-2007-01-05T22:08:00.000Z-Cleanup_needed" class="ext-discussiontools-init-timestamplink">22:08, 5 January 2007 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-MFH-2007-01-05T22:08:00.000Z-Cleanup_needed"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-MFH-2007-01-05T22:08:00.000Z-Cleanup_needed"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Cubed_polynomials_plus_7_imaginary" data-mw-thread-id="h-Cubed_polynomials_plus_7_imaginary-2007-05-08T23:11:00.000Z"><span data-mw-comment-start="" id="h-Cubed_polynomials_plus_7_imaginary-2007-05-08T23:11:00.000Z"></span>Cubed polynomials plus 7 imaginary<span data-mw-comment-end="h-Cubed_polynomials_plus_7_imaginary-2007-05-08T23:11:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=10" title="Edit section: Cubed polynomials plus 7 imaginary"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Gradster1-2007-05-08T23:11:00.000Z-Cubed_polynomials_plus_7_imaginary"></span>This article needs information on how to factor cubed polynomials and also why is it 7 imaginary rather than plus or minus y? </p><p><a href="/wiki/User:Gradster1" title="User:Gradster1">Gradster1</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Gradster1-2007-05-08T23:11:00.000Z-Cubed_polynomials_plus_7_imaginary" class="ext-discussiontools-init-timestamplink">23:11, 8 May 2007 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Gradster1-2007-05-08T23:11:00.000Z-Cubed_polynomials_plus_7_imaginary"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Gradster1-2007-05-08T23:11:00.000Z-Cubed_polynomials_plus_7_imaginary"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Error_in_"other_common_formulas"" data-mw-thread-id="h-Error_in_"other_common_formulas"-2007-09-03T04:49:00.000Z"><span id="Error_in_.22other_common_formulas.22"></span><span data-mw-comment-start="" id="h-Error_in_"other_common_formulas"-2007-09-03T04:49:00.000Z"></span>Error in "other common formulas"<span data-mw-comment-end="h-Error_in_"other_common_formulas"-2007-09-03T04:49:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=11" title="Edit section: Error in "other common formulas""><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-AV-2-2007-09-03T04:49:00.000Z-Error_in_"other_common_formulas""></span>I found a mistake in the fourth formula, it would be good if someone could review the formulas that come after this.<a href="/wiki/User:AV-2" title="User:AV-2">AV-2</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-AV-2-2007-09-03T04:49:00.000Z-Error_in_"other_common_formulas"" class="ext-discussiontools-init-timestamplink">04:49, 3 September 2007 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-AV-2-2007-09-03T04:49:00.000Z-Error_in_"other_common_formulas""><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-AV-2-2007-09-03T04:49:00.000Z-Error_in_"other_common_formulas""></span> </p><p><span data-mw-comment-start="" id="c-211.27.0.27-2009-02-08T05:54:00.000Z-Error_in_"other_common_formulas""></span>BUT IT STILL DIDNT TELL ME WHAT THEY ARE!!!!!!!!!!! </p> <hr/> <p><span style="font-size: smaller;" class="autosigned">—Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/211.27.0.27" title="Special:Contributions/211.27.0.27">211.27.0.27</a> (<a href="/w/index.php?title=User_talk:211.27.0.27&action=edit&redlink=1" class="new" title="User talk:211.27.0.27 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-211.27.0.27-2009-02-08T05:54:00.000Z-Error_in_"other_common_formulas"" class="ext-discussiontools-init-timestamplink">05:54, 8 February 2009 (UTC)</a></span><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-211.27.0.27-2009-02-08T05:54:00.000Z-Error_in_"other_common_formulas""><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-211.27.0.27-2009-02-08T05:54:00.000Z-Error_in_"other_common_formulas""></span> </p><div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Factoring_by_grouping" data-mw-thread-id="h-Factoring_by_grouping-2008-06-24T21:55:00.000Z"><span data-mw-comment-start="" id="h-Factoring_by_grouping-2008-06-24T21:55:00.000Z"></span>Factoring by grouping<span data-mw-comment-end="h-Factoring_by_grouping-2008-06-24T21:55:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=12" title="Edit section: Factoring by grouping"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Brentt-2008-06-24T21:55:00.000Z-Factoring_by_grouping"></span>There is no reason that the factoring by grouping should use a trigonometry example. This unnecessarily excludes students unfamiliar with trigonometry from following the example. <a href="/wiki/User:Brentt" title="User:Brentt">Brentt</a> (<a href="/wiki/User_talk:Brentt" title="User talk:Brentt">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Brentt-2008-06-24T21:55:00.000Z-Factoring_by_grouping" class="ext-discussiontools-init-timestamplink">21:55, 24 June 2008 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Brentt-2008-06-24T21:55:00.000Z-Factoring_by_grouping"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Brentt-2008-06-24T21:55:00.000Z-Factoring_by_grouping"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Last_link_in_the_external_links_section" data-mw-thread-id="h-Last_link_in_the_external_links_section-2009-08-17T15:18:00.000Z"><span data-mw-comment-start="" id="h-Last_link_in_the_external_links_section-2009-08-17T15:18:00.000Z"></span>Last link in the external links section<span data-mw-comment-end="h-Last_link_in_the_external_links_section-2009-08-17T15:18:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=13" title="Edit section: Last link in the external links section"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Almogo-2009-08-17T15:18:00.000Z-Last_link_in_the_external_links_section"></span>Am I the only one who thinks that this is of no value at all and that the entire purpose of that page is to promote their software? Anyone else thinks it should be removed? <a href="/w/index.php?title=User:Almogo&action=edit&redlink=1" class="new" title="User:Almogo (page does not exist)">Almogo</a> (<a href="/wiki/User_talk:Almogo" title="User talk:Almogo">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Almogo-2009-08-17T15:18:00.000Z-Last_link_in_the_external_links_section" class="ext-discussiontools-init-timestamplink">15:18, 17 August 2009 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Almogo-2009-08-17T15:18:00.000Z-Last_link_in_the_external_links_section"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Almogo-2009-08-17T15:18:00.000Z-Last_link_in_the_external_links_section"></span> </p><p><span data-mw-comment-start="" id="c-128.186.122.40-2009-09-17T13:33:00.000Z-Last_link_in_the_external_links_section"></span>I removed it. Not only was it pointed toward vendor software, the connection with factorization was very tenuous. <a href="/wiki/Special:Contributions/128.186.122.40" title="Special:Contributions/128.186.122.40">128.186.122.40</a> (<a href="/w/index.php?title=User_talk:128.186.122.40&action=edit&redlink=1" class="new" title="User talk:128.186.122.40 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-128.186.122.40-2009-09-17T13:33:00.000Z-Last_link_in_the_external_links_section" class="ext-discussiontools-init-timestamplink">13:33, 17 September 2009 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-128.186.122.40-2009-09-17T13:33:00.000Z-Last_link_in_the_external_links_section"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-128.186.122.40-2009-09-17T13:33:00.000Z-Last_link_in_the_external_links_section"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Funny_introduction_to_the_article" data-mw-thread-id="h-Funny_introduction_to_the_article-2009-10-03T23:19:00.000Z"><span data-mw-comment-start="" id="h-Funny_introduction_to_the_article-2009-10-03T23:19:00.000Z"></span>Funny introduction to the article<span data-mw-comment-end="h-Funny_introduction_to_the_article-2009-10-03T23:19:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=14" title="Edit section: Funny introduction to the article"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Trolle3000-2009-10-03T23:19:00.000Z-Funny_introduction_to_the_article"></span>In the introduction part of the article, the following is stated: <br/>"<br/><i> However, factors are not needed to divide evenly because they are still divisible by any number. For example, technically 3 and 8/3 are factors of 8. But, when factoring for tests teachers are looking for the even divisibility of the numbers.<i></i> </i><br/>"<br/> This seems to be written with certain math tests in mind, and I don't think it is relevant for the article as a whole. Any objections to deleting that part? </p><p><a href="/wiki/User:Trolle3000" title="User:Trolle3000">Trolle3000</a> (<a href="/wiki/User_talk:Trolle3000" title="User talk:Trolle3000">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Trolle3000-2009-10-03T23:19:00.000Z-Funny_introduction_to_the_article" class="ext-discussiontools-init-timestamplink">23:19, 3 October 2009 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Trolle3000-2009-10-03T23:19:00.000Z-Funny_introduction_to_the_article"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Trolle3000-2009-10-03T23:19:00.000Z-Funny_introduction_to_the_article"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-EmilJ-2009-10-05T10:52:00.000Z-Trolle3000-2009-10-03T23:19:00.000Z"></span>The sentence is misleading and completely misguided. In the ring of integers, 3 does not divide 8, period. In the ring of rationals, 3 and 8/3 are true factors of 8, not just "technically". What particular teachers are looking for in particular tests is irrelevant. — <a href="/wiki/User:EmilJ" title="User:EmilJ">Emil</a> <a href="/wiki/User_talk:EmilJ" title="User talk:EmilJ">J.</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-EmilJ-2009-10-05T10:52:00.000Z-Trolle3000-2009-10-03T23:19:00.000Z" class="ext-discussiontools-init-timestamplink">10:52, 5 October 2009 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-EmilJ-2009-10-05T10:52:00.000Z-Trolle3000-2009-10-03T23:19:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-EmilJ-2009-10-05T10:52:00.000Z-Trolle3000-2009-10-03T23:19:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="I_think_this_page_requires_clean-up_and/or_attention" data-mw-thread-id="h-I_think_this_page_requires_clean-up_and/or_attention-2009-10-17T23:54:00.000Z"><span id="I_think_this_page_requires_clean-up_and.2For_attention"></span><span data-mw-comment-start="" id="h-I_think_this_page_requires_clean-up_and/or_attention-2009-10-17T23:54:00.000Z"></span>I think this page requires clean-up and/or attention<span data-mw-comment-end="h-I_think_this_page_requires_clean-up_and/or_attention-2009-10-17T23:54:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=15" title="Edit section: I think this page requires clean-up and/or attention"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Xali-2009-10-17T23:54:00.000Z-I_think_this_page_requires_clean-up_and/or_attention"></span>At least the talk page does; lots of old requests or concerns on this page seem to be unattended.<br/> <br/> Also I added the factor theorem. I was surprised to find it missing in the other section (along with some recently added content that doesn't seem to make any sense...<br/> --<a href="/wiki/User:Xali" title="User:Xali">Xali</a> (<a href="/wiki/User_talk:Xali" title="User talk:Xali">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Xali-2009-10-17T23:54:00.000Z-I_think_this_page_requires_clean-up_and/or_attention" class="ext-discussiontools-init-timestamplink">23:54, 17 October 2009 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Xali-2009-10-17T23:54:00.000Z-I_think_this_page_requires_clean-up_and/or_attention"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Xali-2009-10-17T23:54:00.000Z-I_think_this_page_requires_clean-up_and/or_attention"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Discuss_the_usage_difference_between_"factor"_and_"factorization"" data-mw-thread-id="h-Discuss_the_usage_difference_between_"factor"_and_"factorization"-2010-08-15T19:34:00.000Z"><span id="Discuss_the_usage_difference_between_.22factor.22_and_.22factorization.22"></span><span data-mw-comment-start="" id="h-Discuss_the_usage_difference_between_"factor"_and_"factorization"-2010-08-15T19:34:00.000Z"></span>Discuss the usage difference between "factor" and "factorization"<span data-mw-comment-end="h-Discuss_the_usage_difference_between_"factor"_and_"factorization"-2010-08-15T19:34:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=16" title="Edit section: Discuss the usage difference between "factor" and "factorization""><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-18.111.42.150-2010-08-15T19:34:00.000Z-Discuss_the_usage_difference_between_"factor"_and_"factorization""></span>The two are equivalent, though I would like to know where/when each term was popular. <a href="/wiki/Special:Contributions/18.111.42.150" title="Special:Contributions/18.111.42.150">18.111.42.150</a> (<a href="/w/index.php?title=User_talk:18.111.42.150&action=edit&redlink=1" class="new" title="User talk:18.111.42.150 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-18.111.42.150-2010-08-15T19:34:00.000Z-Discuss_the_usage_difference_between_"factor"_and_"factorization"" class="ext-discussiontools-init-timestamplink">19:34, 15 August 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-18.111.42.150-2010-08-15T19:34:00.000Z-Discuss_the_usage_difference_between_"factor"_and_"factorization""><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-18.111.42.150-2010-08-15T19:34:00.000Z-Discuss_the_usage_difference_between_"factor"_and_"factorization""></span> </p> <dl><dd><span data-mw-comment-start="" id="c-EmilJ-2010-08-16T12:39:00.000Z-18.111.42.150-2010-08-15T19:34:00.000Z"></span>The two are not equivalent. For example, 7 · 11 · 13 is the prime factorization of 1001, whereas 7 (as well as 11 or 13) is a prime factor of 1001.—<a href="/wiki/User:EmilJ" title="User:EmilJ">Emil</a> <a href="/wiki/User_talk:EmilJ" title="User talk:EmilJ">J.</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-EmilJ-2010-08-16T12:39:00.000Z-18.111.42.150-2010-08-15T19:34:00.000Z" class="ext-discussiontools-init-timestamplink">12:39, 16 August 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-EmilJ-2010-08-16T12:39:00.000Z-18.111.42.150-2010-08-15T19:34:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-EmilJ-2010-08-16T12:39:00.000Z-18.111.42.150-2010-08-15T19:34:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Does_Factorization_serve_a_practical_purpose?" data-mw-thread-id="h-Does_Factorization_serve_a_practical_purpose?-2011-11-14T23:48:00.000Z"><span id="Does_Factorization_serve_a_practical_purpose.3F"></span><span data-mw-comment-start="" id="h-Does_Factorization_serve_a_practical_purpose?-2011-11-14T23:48:00.000Z"></span>Does Factorization serve a practical purpose?<span data-mw-comment-end="h-Does_Factorization_serve_a_practical_purpose?-2011-11-14T23:48:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=17" title="Edit section: Does Factorization serve a practical purpose?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Fxm12-2011-11-14T23:48:00.000Z-Does_Factorization_serve_a_practical_purpose?"></span>Does it have a use? <a href="/wiki/User:Fxm12" title="User:Fxm12">Fxm12</a> (<a href="/wiki/User_talk:Fxm12" title="User talk:Fxm12">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Fxm12-2011-11-14T23:48:00.000Z-Does_Factorization_serve_a_practical_purpose?" class="ext-discussiontools-init-timestamplink">23:48, 14 November 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Fxm12-2011-11-14T23:48:00.000Z-Does_Factorization_serve_a_practical_purpose?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Fxm12-2011-11-14T23:48:00.000Z-Does_Factorization_serve_a_practical_purpose?"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Hári_Zalán-20230306100100-Fxm12-2011-11-14T23:48:00.000Z"></span>Yes, it does: the <a href="/wiki/RSA_(cryptosystem)" title="RSA (cryptosystem)">RSA</a> is based on factorisation of large numbers is very slow. <a href="/wiki/User:H%C3%A1ri_Zal%C3%A1n" title="User:Hári Zalán">Hári Zalán</a> (<a href="/wiki/User_talk:H%C3%A1ri_Zal%C3%A1n" title="User talk:Hári Zalán">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Hári_Zalán-20230306100100-Fxm12-2011-11-14T23:48:00.000Z" class="ext-discussiontools-init-timestamplink">10:01, 6 March 2023 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Hári_Zalán-20230306100100-Fxm12-2011-11-14T23:48:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Hári_Zalán-20230306100100-Fxm12-2011-11-14T23:48:00.000Z"></span></dd></dl> <p><span data-mw-comment-start="" id="c-Dagme-2014-05-01T02:15:00.000Z-Does_Factorization_serve_a_practical_purpose?"></span>Keeps teachers employed. (Just kidding --- couldn't resist.) --<a href="/wiki/User:Dagme" title="User:Dagme">Dagme</a> (<a href="/wiki/User_talk:Dagme" title="User talk:Dagme">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Dagme-2014-05-01T02:15:00.000Z-Does_Factorization_serve_a_practical_purpose?" class="ext-discussiontools-init-timestamplink">02:15, 1 May 2014 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Dagme-2014-05-01T02:15:00.000Z-Does_Factorization_serve_a_practical_purpose?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Dagme-2014-05-01T02:15:00.000Z-Does_Factorization_serve_a_practical_purpose?"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="LaTeX_Code?" data-mw-thread-id="h-LaTeX_Code?-2014-05-01T02:14:00.000Z"><span id="LaTeX_Code.3F"></span><span data-mw-comment-start="" id="h-LaTeX_Code?-2014-05-01T02:14:00.000Z"></span>LaTeX Code?<span data-mw-comment-end="h-LaTeX_Code?-2014-05-01T02:14:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=18" title="Edit section: LaTeX Code?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Dagme-2014-05-01T02:14:00.000Z-LaTeX_Code?"></span>Is there a way to export LaTeX Code from Wikipedia articles such as this? --<a href="/wiki/User:Dagme" title="User:Dagme">Dagme</a> (<a href="/wiki/User_talk:Dagme" title="User talk:Dagme">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Dagme-2014-05-01T02:14:00.000Z-LaTeX_Code?" class="ext-discussiontools-init-timestamplink">02:14, 1 May 2014 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Dagme-2014-05-01T02:14:00.000Z-LaTeX_Code?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Dagme-2014-05-01T02:14:00.000Z-LaTeX_Code?"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Refactoring_and_adding_references" data-mw-thread-id="h-Refactoring_and_adding_references-2014-11-03T18:50:00.000Z"><span data-mw-comment-start="" id="h-Refactoring_and_adding_references-2014-11-03T18:50:00.000Z"></span>Refactoring and adding references<span data-mw-comment-end="h-Refactoring_and_adding_references-2014-11-03T18:50:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=19" title="Edit section: Refactoring and adding references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Wcherowi-2014-11-03T18:50:00.000Z-Refactoring_and_adding_references"></span>I have started a refactor of this page. The page, as originally envisioned (as I see it), was a gentle introduction to elementary factoring techniques. It was well done and was decently structured (but never completed). Over time, additions by various editors have disrupted the coherence of the article and introduced some subtle errors. In thinking about how to fix the page it became clear to me that the original organizing principle (doing a thorough job with quadratics in one variable and then move on to more complex polynomials) was too limiting for an encyclopedic article (it would be ok in a textbook). Thus, I am scrapping the original approach in reorganizing this page. I hope to keep the level of the article about the same and I will reuse all the quadratic stuff as examples. This will take a little time. <a href="/wiki/User:Wcherowi" title="User:Wcherowi">Bill Cherowitzo </a> (<a href="/wiki/User_talk:Wcherowi" title="User talk:Wcherowi">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Wcherowi-2014-11-03T18:50:00.000Z-Refactoring_and_adding_references" class="ext-discussiontools-init-timestamplink">18:50, 3 November 2014 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Wcherowi-2014-11-03T18:50:00.000Z-Refactoring_and_adding_references"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Wcherowi-2014-11-03T18:50:00.000Z-Refactoring_and_adding_references"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Assessment_comment" data-mw-thread-id="h-Assessment_comment-2006-10-05T14:56:00.000Z"><span data-mw-comment-start="" id="h-Assessment_comment-2006-10-05T14:56:00.000Z"></span>Assessment comment<span data-mw-comment-end="h-Assessment_comment-2006-10-05T14:56:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=20" title="Edit section: Assessment comment"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div><p><span data-mw-comment-start="" id="c-Tompw-2006-10-05T14:56:00.000Z-Assessment_comment"></span> The comment(s) below were originally left at <span class="plainlinks"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Talk:Factorization/Comments&redirect=no">Talk:Factorization/Comments</a></span>, and are posted here for posterity. Following <a href="/wiki/Wikipedia:DCS" class="mw-redirect" title="Wikipedia:DCS">several discussions in past years</a>, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.</p><table style="width:100%; background-color:#eaf8f4; border-left:3px solid #008560;"><tbody><tr><td colspan="2">Needs more prose to accompany equations; some sections need expanding <a href="/wiki/User:Tompw" title="User:Tompw">Tompw</a> <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Tompw-2006-10-05T14:56:00.000Z-Assessment_comment" class="ext-discussiontools-init-timestamplink">14:56, 5 October 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Tompw-2006-10-05T14:56:00.000Z-Assessment_comment"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Tompw-2006-10-05T14:56:00.000Z-Assessment_comment"></span></td></tr> </tbody></table> <p>Last edited at 23:41, 19 April 2007 (UTC). Substituted at 02:05, 5 May 2016 (UTC) </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Separating_univariate_polynomial_factorization_from_bivariate_polynomial_factorization" data-mw-thread-id="h-Separating_univariate_polynomial_factorization_from_bivariate_polynomial_factori-2017-09-15T16:52:00.000Z"><span data-mw-comment-start="" id="h-Separating_univariate_polynomial_factorization_from_bivariate_polynomial_factori-2017-09-15T16:52:00.000Z"></span>Separating univariate polynomial factorization from bivariate polynomial factorization<span data-mw-comment-end="h-Separating_univariate_polynomial_factorization_from_bivariate_polynomial_factori-2017-09-15T16:52:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=21" title="Edit section: Separating univariate polynomial factorization from bivariate polynomial factorization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Loraof-2017-09-15T16:52:00.000Z-Separating_univariate_polynomial_factorization_from_bivariate_polynomial_factori"></span>Right now in the main (polynomials) part of the article, the sequence of subsections randomly alternates between univariate (U below), bivariate (B below), and trivariate (T below) polynomials as follows: </p> <dl><dd>BBUUUBBBBBBTUB</dd></dl> <p>I'm going to rearrange this to put all the univariate subsections first. <a href="/wiki/User:Loraof" title="User:Loraof">Loraof</a> (<a href="/wiki/User_talk:Loraof" title="User talk:Loraof">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Loraof-2017-09-15T16:52:00.000Z-Separating_univariate_polynomial_factorization_from_bivariate_polynomial_factori" class="ext-discussiontools-init-timestamplink">16:52, 15 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Loraof-2017-09-15T16:52:00.000Z-Separating_univariate_polynomial_factorization_from_bivariate_polynomial_factori"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Loraof-2017-09-15T16:52:00.000Z-Separating_univariate_polynomial_factorization_from_bivariate_polynomial_factori"></span> </p> <dl><dd><span class="template-ping"><small style="font-style:italic;font-weight:bold;"><span data-mw-comment-start="" id="c-D.Lazard-2017-09-15T17:35:00.000Z-Loraof-2017-09-15T16:52:00.000Z"></span>To</small> editor <a href="/wiki/User:Loraof" title="User:Loraof">Loraof</a>:</span> There is another important issue in the polynomial part of the article: although it refers to <a href="/wiki/Polynomial_factorization" class="mw-redirect" title="Polynomial factorization">Polynomial factorization</a> through a <span class="nowrap">{{</span><a href="/wiki/Template:Main" title="Template:Main">main</a><span class="nowrap">}}</span> template, its content differs dramatically from the content of the main article (normally, the content of a section with a template <span class="nowrap">{{</span><a href="/wiki/Template:Main" title="Template:Main">main</a><span class="nowrap">}}</span> should be a summary of the main article). Moreover, there is a <a href="/wiki/Wikipedia:UNDUE" class="mw-redirect" title="Wikipedia:UNDUE">undue weight</a> given to methods that are used only in elementary teaching, and nowhere else; this is misleading, because a reader who do not read the article carefully may ignore that the theory of polynomial factorization is an active area of research, and that a large part part of this theory is interesting at elementary level (for example primpart-content factorization and square-free factorization).</dd> <dd>Therefore, IMO, the article deserve more work than simply permuting sections. <a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-D.Lazard-2017-09-15T17:35:00.000Z-Loraof-2017-09-15T16:52:00.000Z" class="ext-discussiontools-init-timestamplink">17:35, 15 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-2017-09-15T17:35:00.000Z-Loraof-2017-09-15T16:52:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-D.Lazard-2017-09-15T17:35:00.000Z-Loraof-2017-09-15T16:52:00.000Z"></span></dd></dl> <dl><dd><dl><dd><span data-mw-comment-start="" id="c-Loraof-2017-09-15T20:14:00.000Z-D.Lazard-2017-09-15T17:35:00.000Z"></span>Okay. The present article has almost nothing about factorization of anything but polynomials, and the substantial majority of it is about bivariate polynomials, while <a href="/wiki/Polynomial_factorization" class="mw-redirect" title="Polynomial factorization">Polynomial factorization</a> is exclusively about univariate polynomials.</dd></dl></dd></dl> <dl><dd><dl><dd>Therefore, I propose to turn the present article, <a href="/wiki/Factorization" title="Factorization">Factorization</a>, into an article called <a href="/w/index.php?title=Factorization_of_bivariate_polynomials&action=edit&redlink=1" class="new" title="Factorization of bivariate polynomials (page does not exist)">Factorization of bivariate polynomials</a>, and to move the present article's content on univariate polynomials over to <a href="/wiki/Polynomial_factorization" class="mw-redirect" title="Polynomial factorization">Polynomial factorization</a>. What do you think? <a href="/wiki/User:Loraof" title="User:Loraof">Loraof</a> (<a href="/wiki/User_talk:Loraof" title="User talk:Loraof">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Loraof-2017-09-15T20:14:00.000Z-D.Lazard-2017-09-15T17:35:00.000Z" class="ext-discussiontools-init-timestamplink">20:14, 15 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Loraof-2017-09-15T20:14:00.000Z-D.Lazard-2017-09-15T17:35:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Loraof-2017-09-15T20:14:00.000Z-D.Lazard-2017-09-15T17:35:00.000Z"></span> <dl><dd><span class="template-ping"><small style="font-style:italic;font-weight:bold;"><span data-mw-comment-start="" id="c-D.Lazard-2017-09-17T09:37:00.000Z-Loraof-2017-09-15T20:14:00.000Z"></span>To</small> editor <a href="/wiki/User:Loraof" title="User:Loraof">Loraof</a>:</span> I have reread the article. I agree that some refactoring could be useful. However, the sections that you call "bivariate" are not really about the bivariate case; instead they refer either to the general multivariate case, with examples that are simply bivariate, such as the section about the factorization of monomials, or they present patterns referring to two subexpressions. In fact, the authors of the article use <i>x</i>, <i>y</i>, ... for indeterminates, and <i>a</i>, <i>b</i>, ... for subexpressions occurring in patterns (this would deserve to be explicitly said). Thus the classification could be between sections strictly devoted to univariate case and sections where the number of variables does not matter. For me, it is unclear, if this ordering is, or not, better than an order based on an increasing technicality.</dd> <dd>About the move: you are wrong when saying that <a href="/wiki/Polynomial_factorization" class="mw-redirect" title="Polynomial factorization">Polynomial factorization</a> is only about the univariate case; it shows that the multivariate case reduces to univariate case through a recursion on the number of variables. Therefore, I suggest rather to move the article to <a href="/w/index.php?title=Factorization_(hand-written)&action=edit&redlink=1" class="new" title="Factorization (hand-written) (page does not exist)">Factorization (hand-written)</a>. <a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-D.Lazard-2017-09-17T09:37:00.000Z-Loraof-2017-09-15T20:14:00.000Z" class="ext-discussiontools-init-timestamplink">09:37, 17 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-2017-09-17T09:37:00.000Z-Loraof-2017-09-15T20:14:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-D.Lazard-2017-09-17T09:37:00.000Z-Loraof-2017-09-15T20:14:00.000Z"></span></dd></dl></dd></dl></dd></dl> <dl><dd><dl><dd><dl><dd><dl><dd><span data-mw-comment-start="" id="c-Loraof-2017-09-17T19:19:00.000Z-D.Lazard-2017-09-17T09:37:00.000Z"></span>Okay, how about if I rename this article <a href="/w/index.php?title=Factorization_of_polynomials_by_hand&action=edit&redlink=1" class="new" title="Factorization of polynomials by hand (page does not exist)">Factorization of polynomials by hand</a>, remove the essentially contentless sections not about polynomials, and after the section on basic concepts put a section on univariate polynomials followed by a section on multivariate polynomials, mentioning that <i>a</i> and <i>b</i> can be indeterminates or polynomials? <a href="/wiki/User:Loraof" title="User:Loraof">Loraof</a> (<a href="/wiki/User_talk:Loraof" title="User talk:Loraof">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Loraof-2017-09-17T19:19:00.000Z-D.Lazard-2017-09-17T09:37:00.000Z" class="ext-discussiontools-init-timestamplink">19:19, 17 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Loraof-2017-09-17T19:19:00.000Z-D.Lazard-2017-09-17T09:37:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Loraof-2017-09-17T19:19:00.000Z-D.Lazard-2017-09-17T09:37:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-D.Lazard-2017-09-19T13:28:00.000Z-Loraof-2017-09-17T19:19:00.000Z"></span>Before moving this article, we should examine what doing with its title. In fact, "Factorization" is probably the first term which is searched when searching for either factorization of integers, or polynomials, or other kinds of objects. therefore, the tilt must be kept. Since all these subjects are strongly related, a dab page is not convenient. A <a href="/wiki/Wikipedia:Broad-concept_article" title="Wikipedia:Broad-concept article">WP:broad-concept article</a>, would be possible; however the spirit of broad-concept article is being a kind of stub <i>before</i> writing a more developed article. This article looks like a broad concept article that has been developed for one of its aspects (polynomials) but not for the others (integers and other kinds of objects cited in the lead). I understand your suggestion as splitting the article into a broad-concept article, and a new article on polynomials. However, it would leave empty or almost empty the description of other factorizations cited in the lead.</dd> <dd>On the other hand <a href="/wiki/Integer_factorization" title="Integer factorization">Integer factorization</a> is only about algorithms, and I have not found any article describing the elementary methods (test of divisibility by 2, 3, 5, 11, and its use for <a href="/wiki/Trial_division" title="Trial division">trial divisions</a>; <a href="/wiki/Sieve_of_Eratosthenes" title="Sieve of Eratosthenes">Sieve of Eratosthenes</a>, and its use for trial divisions, etc.).</dd> <dd>For these reasons, I'll put clearer hatnotes to the sections, and <span class="nowrap">{{</span><a href="/wiki/Template:Expand_section" title="Template:Expand section">expand section</a><span class="nowrap">}}</span> tags, with explanation of the desired content of such expansion. IMO, it is more important to expand these almost empty sections than moving the article.<a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-D.Lazard-2017-09-19T13:28:00.000Z-Loraof-2017-09-17T19:19:00.000Z" class="ext-discussiontools-init-timestamplink">13:28, 19 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-2017-09-19T13:28:00.000Z-Loraof-2017-09-17T19:19:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-D.Lazard-2017-09-19T13:28:00.000Z-Loraof-2017-09-17T19:19:00.000Z"></span></dd></dl></dd></dl></dd></dl></dd></dl></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Rewriting_this_article" data-mw-thread-id="h-Rewriting_this_article-2018-03-21T14:44:00.000Z"><span data-mw-comment-start="" id="h-Rewriting_this_article-2018-03-21T14:44:00.000Z"></span>Rewriting this article<span data-mw-comment-end="h-Rewriting_this_article-2018-03-21T14:44:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=22" title="Edit section: Rewriting this article"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-D.Lazard-2018-03-21T14:44:00.000Z-Rewriting_this_article"></span>I know, for a long time that this is article was a mess (see the above thread). A recent edit by <a href="/w/index.php?title=User:Magyar25&action=edit&redlink=1" class="new" title="User:Magyar25 (page does not exist)">Magyar25</a> showed me that it was full of mathematical errors an <a href="/wiki/Wikipedia:OR" class="mw-redirect" title="Wikipedia:OR">WP:OR</a> opinions, mainly that a factorization must produce a simplification. Therefore I have rewritten the lead and the integer section, and started to rewrite the section on polynomials (not yet published). Doing that, I remarked another issue of this article: several hatnotes (there were too many) asserted that the article intends to be elementary. In fact, the simplest algebraic manipulations are detailed as if this were a first textbook for learning algebraic manipulations, and so many details are given that the main points become confusing. In the same time, the reader that is not supposed knowing simple algebraic manipulations is supposed to know what is a polynomial and what is the efficiency of a computation. Thinking about this, it appeared to me that the long section about factorization of polynomials was, in fact about factorization of <i>expressions</i>, as all methods apply when, for example, trigonometric functions are involved. </p><p>For these reasons, I have started to rewrite the whole article, keeping it at least as elementary as it was, but placing it in the right mathematical context, and, when it is relevant, giving some insight toward more sophistical concepts. I hope that the result will be convenient for beginners, as well as for mathematicians. <a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-D.Lazard-2018-03-21T14:44:00.000Z-Rewriting_this_article" class="ext-discussiontools-init-timestamplink">14:44, 21 March 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-2018-03-21T14:44:00.000Z-Rewriting_this_article"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-D.Lazard-2018-03-21T14:44:00.000Z-Rewriting_this_article"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-D.Lazard-2018-03-26T17:58:00.000Z-D.Lazard-2018-03-21T14:44:00.000Z"></span><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/fb/Yes_check.svg/18px-Yes_check.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/fb/Yes_check.svg/27px-Yes_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/fb/Yes_check.svg/36px-Yes_check.svg.png 2x" data-file-width="600" data-file-height="600"/></span></span><b> Done</b></span>. The announced rewrite is now complete. <a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-D.Lazard-2018-03-26T17:58:00.000Z-D.Lazard-2018-03-21T14:44:00.000Z" class="ext-discussiontools-init-timestamplink">17:58, 26 March 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-2018-03-26T17:58:00.000Z-D.Lazard-2018-03-21T14:44:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-D.Lazard-2018-03-26T17:58:00.000Z-D.Lazard-2018-03-21T14:44:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Error" data-mw-thread-id="h-Error-2018-09-12T23:21:00.000Z"><span data-mw-comment-start="" id="h-Error-2018-09-12T23:21:00.000Z"></span>Error<span data-mw-comment-end="h-Error-2018-09-12T23:21:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=23" title="Edit section: Error"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-86.82.164.5-2018-09-12T23:21:00.000Z-Error"></span>A small remark from a non-expert: I am quite certain the Fermat number 2**32+1 is 4294967297 and not 4295967297 as mentioned in the text. I think this is an error and should be corrected. [R.m.c. Ahn] <small class="autosigned">— Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/86.82.164.5" title="Special:Contributions/86.82.164.5">86.82.164.5</a> (<a href="/w/index.php?title=User_talk:86.82.164.5&action=edit&redlink=1" class="new" title="User talk:86.82.164.5 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-86.82.164.5-2018-09-12T23:21:00.000Z-Error" class="ext-discussiontools-init-timestamplink">23:21, 12 September 2018 (UTC)</a></small><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-86.82.164.5-2018-09-12T23:21:00.000Z-Error"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-86.82.164.5-2018-09-12T23:21:00.000Z-Error"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Wcherowi-2018-09-13T03:55:00.000Z-86.82.164.5-2018-09-12T23:21:00.000Z"></span><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/fb/Yes_check.svg/18px-Yes_check.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/fb/Yes_check.svg/27px-Yes_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/fb/Yes_check.svg/36px-Yes_check.svg.png 2x" data-file-width="600" data-file-height="600"/></span></span><b> Done</b></span>. Good catch. --<a href="/wiki/User:Wcherowi" title="User:Wcherowi">Bill Cherowitzo </a> (<a href="/wiki/User_talk:Wcherowi" title="User talk:Wcherowi">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Wcherowi-2018-09-13T03:55:00.000Z-86.82.164.5-2018-09-12T23:21:00.000Z" class="ext-discussiontools-init-timestamplink">03:55, 13 September 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Wcherowi-2018-09-13T03:55:00.000Z-86.82.164.5-2018-09-12T23:21:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Wcherowi-2018-09-13T03:55:00.000Z-86.82.164.5-2018-09-12T23:21:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Add_Factorisation_by_inspection_section_to_polynomial_section" data-mw-thread-id="h-Add_Factorisation_by_inspection_section_to_polynomial_section-20230519013900"><span data-mw-comment-start="" id="h-Add_Factorisation_by_inspection_section_to_polynomial_section-20230519013900"></span>Add Factorisation by inspection section to polynomial section<span data-mw-comment-end="h-Add_Factorisation_by_inspection_section_to_polynomial_section-20230519013900"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Factorization&action=edit&section=24" title="Edit section: Add Factorisation by inspection section to polynomial section"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Raakkk-20230519013900-Add_Factorisation_by_inspection_section_to_polynomial_section"></span>Request to add "factorisation by inspection" to factorising polynomials section. This method uses abstracted concepts from factor theorum method, deserves its own section. <a href="/w/index.php?title=User:Raakkk&action=edit&redlink=1" class="new" title="User:Raakkk (page does not exist)">Raakkk</a> (<a href="/w/index.php?title=User_talk:Raakkk&action=edit&redlink=1" class="new" title="User talk:Raakkk (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-Raakkk-20230519013900-Add_Factorisation_by_inspection_section_to_polynomial_section" class="ext-discussiontools-init-timestamplink">01:39, 19 May 2023 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Raakkk-20230519013900-Add_Factorisation_by_inspection_section_to_polynomial_section"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Raakkk-20230519013900-Add_Factorisation_by_inspection_section_to_polynomial_section"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-87.117.87.35-20230921183100-Raakkk-20230519013900"></span>What size is it please <a href="/wiki/Special:Contributions/87.117.87.35" title="Special:Contributions/87.117.87.35">87.117.87.35</a> (<a href="/w/index.php?title=User_talk:87.117.87.35&action=edit&redlink=1" class="new" title="User talk:87.117.87.35 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-87.117.87.35-20230921183100-Raakkk-20230519013900" class="ext-discussiontools-init-timestamplink">18:31, 21 September 2023 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-87.117.87.35-20230921183100-Raakkk-20230519013900"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-87.117.87.35-20230921183100-Raakkk-20230519013900"></span> <dl><dd><span data-mw-comment-start="" id="c-87.117.87.35-20230921183300-87.117.87.35-20230921183100"></span>I don't understand what size is ìt can you explain to the si <a href="/wiki/Special:Contributions/87.117.87.35" title="Special:Contributions/87.117.87.35">87.117.87.35</a> (<a href="/w/index.php?title=User_talk:87.117.87.35&action=edit&redlink=1" class="new" title="User talk:87.117.87.35 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-87.117.87.35-20230921183300-87.117.87.35-20230921183100" class="ext-discussiontools-init-timestamplink">18:33, 21 September 2023 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-87.117.87.35-20230921183300-87.117.87.35-20230921183100"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-87.117.87.35-20230921183300-87.117.87.35-20230921183100"></span></dd></dl></dd> <dd><span data-mw-comment-start="" id="c-D.Lazard-20230921204200-Raakkk-20230519013900"></span>A source is needed for including the method. I have never heard of a "factor theorum method". As far as I know, "factorization by inspection" cannot be very different from the content of section <a href="/wiki/Factorization#Recognizable_patterns" title="Factorization">§ Recognizable patterns</a>. If I am wrong, please, clarify your meaning of "factorization by inspection". <a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Factorization#c-D.Lazard-20230921204200-Raakkk-20230519013900" class="ext-discussiontools-init-timestamplink">20:42, 21 September 2023 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-20230921204200-Raakkk-20230519013900"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-D.Lazard-20230921204200-Raakkk-20230519013900"></span></dd></dl>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Talk:Factorization&oldid=1241244370">https://en.wikipedia.org/w/index.php?title=Talk:Factorization&oldid=1241244370</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:C-Class_mathematics_articles" title="Category:C-Class mathematics articles">C-Class mathematics articles</a></li><li><a href="/wiki/Category:Mid-priority_mathematics_articles" title="Category:Mid-priority mathematics articles">Mid-priority mathematics articles</a></li><li><a href="/wiki/Category:C-Class_Numbers_articles" title="Category:C-Class Numbers articles">C-Class Numbers articles</a></li><li><a href="/wiki/Category:Unknown-importance_Numbers_articles" title="Category:Unknown-importance Numbers articles">Unknown-importance Numbers articles</a></li><li><a href="/wiki/Category:WikiProject_Numbers_articles" title="Category:WikiProject Numbers articles">WikiProject Numbers articles</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 20 August 2024, at 04:27<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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