{"id":84,"date":"2005-06-19T14:50:50","date_gmt":"2005-06-19T14:50:50","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=84"},"modified":"2005-06-19T14:50:50","modified_gmt":"2005-06-19T14:50:50","slug":"polynomial-division","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=84","title":{"rendered":"Polynomial Division"},"content":{"rendered":"<p>A long time ago UK students used to learn how to do polynomial long division before they were 16. Nowadays, they see little of it until they reach A level, and the new national syllabus expects them to learn the remainder theorem for AS (16+). They don&#8217;t actually need to do long division as examples are usually simple enough to allow one to guess factors; for example <img src='\/maths\/latexrender\/pictures\/d8ce9bdf6c9cd094cd8e1f8c38ad9404.gif' title='x^3-7x+6=(x-1)(x^2+ax-6)' alt='x^3-7x+6=(x-1)(x^2+ax-6)' align=absmiddle> and <img src='\/maths\/latexrender\/pictures\/0cc175b9c0f1b6a831c399e269772661.gif' title='a' alt='a' align=absmiddle> has to be found. Nevertheless, it is useful to be able to do long division and, given the time constraints, I usually use <a href=\"http:\/\/www.sixthform.info\/steve\/maths\/synthetic.htm\" target=\"_blank\">Synthetic Division<\/a>.<\/p>\n<p><img src='\/maths\/latexrender\/pictures\/c51d7e23458ca0e7373a8ed6ab56b2b9.gif' title='\\LaTeX' alt='\\LaTeX' align=absmiddle> allows you not only to show the steps of either method, it will also do the mathematics for you, thanks to the <a href=\"http:\/\/www.ctan.org\/tex-archive\/help\/Catalogue\/entries\/polynom.html\" target=\"_blank\">polynom<\/a> package. The code <font face=\"courier new, courier, mono\" size=\"2\">\\polylongdiv{x^3-7x+6}{x-1}<\/font> produces <\/p>\n<ul><img src='\/maths\/latexrender\/pictures\/d4d8c2e6d38fb2a655b7bfeecc0a84b4.gif' title='\\polylongdiv{x^3-7x+6}{x-1}' alt='\\polylongdiv{x^3-7x+6}{x-1}' align=absmiddle><\/ul>\n<p> and <font face=\"courier new, courier, mono\" size=\"2\">\\polyhornerscheme[x=1]{x^3-7x+6}<\/font> gives <\/p>\n<ul><img src='\/maths\/latexrender\/pictures\/0c5e48d1e6dc34e545214031b1df20fe.gif' title='\\polyhornerscheme[x=1]{x^3-7x+6}' alt='\\polyhornerscheme[x=1]{x^3-7x+6}' align=absmiddle><\/ul>\n<p> There&#8217;s lots more possibilities such as <\/p>\n<ul><img src='\/maths\/latexrender\/pictures\/22a3dbebf1d5c92b10d574fbd7bdacb4.gif' title='\\polyhornerscheme[x=1,tutor=true,resultstyle=\\color{blue},tutorlimit=8,stage=8]{x^3-7x+6}' alt='\\polyhornerscheme[x=1,tutor=true,resultstyle=\\color{blue},tutorlimit=8,stage=8]{x^3-7x+6}' align=absmiddle><\/ul>\n<p>Brilliant! You can watch an online demo of the polynom package doing division step-by-step in a number of different ways <a href=\"http:\/\/www.ctan.org\/tex-archive\/macros\/latex\/contrib\/polynom\/polydemo.pdf\" target=\"_blank\">here<\/a>. Click to move the demo on, press Esc to end it.<\/p>\n<p><i>Please note: \\polyhornerscheme is not available in versions of polynom before version 0.16, so if you wish to use \\polyhornerscheme do make sure you get the latest version, perhaps from <a href=\"http:\/\/texcatalogue.sarovar.org\/entries\/polynom.html\" target=\"_blank\">here<\/a><\/i><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A long time ago UK students used to learn how to do polynomial long division before they were 16. Nowadays, they see little of it until they reach A level, and the new national syllabus expects them to learn the remainder theorem for AS (16+). They don&#8217;t actually need to do long division as examples [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-84","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/84","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=84"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/84\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=84"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=84"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}