{"id":6899,"date":"2011-06-06T23:02:50","date_gmt":"2011-06-06T22:02:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6899"},"modified":"2022-01-10T22:28:01","modified_gmt":"2022-01-10T22:28:01","slug":"decompoe-em-factores-os-polinomios","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6899","title":{"rendered":"Decomp\u00f5e em fatores os polin\u00f3mios"},"content":{"rendered":"<p><ul id='GTTabs_ul_6899' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6899' class='GTTabs_curr'><a  id=\"6899_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6899' ><a  id=\"6899_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6899'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Decomp\u00f5e em fatores os polin\u00f3mios:<\/p>\n<ol>\n<li>${{x}^{2}}-6x+9$<\/li>\n<li>$4{{x}^{2}}+4x+1$<\/li>\n<li>${{a}^{2}}+2ab+{{b}^{2}}$<\/li>\n<li>${{y}^{2}}-25$<\/li>\n<li>$4{{a}^{2}}-1$<\/li>\n<li>$8{{x}^{3}}y-2x{{y}^{3}}$<\/li>\n<li>$2{{x}^{2}}+12x+18$<\/li>\n<li>$3{{a}^{2}}x+6ax+3x$<\/li>\n<li>${{x}^{3}}-x$<\/li>\n<li>${{a}^{2}}(a-2)-2a(a-2)+(a-2)$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6899' onClick='GTTabs_show(1,6899)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6899'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n{{x}^{2}}-6x+9 &amp; = &amp; {{(x-3)}^{2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; (x-3)(x-3)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n4{{x}^{2}}+4x+1 &amp; = &amp; {{(2x+1)}^{2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; (2x+1)(2x+1)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n{{a}^{2}}+2ab+{{b}^{2}} &amp; = &amp; {{(a+b)}^{2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; (a+b)(a+b)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<li>Ora,<br \/>\n${{y}^{2}}-25=(y+5)(y-5)$<\/li>\n<li>Ora,<br \/>\n$4{{a}^{2}}-1=(2a+1)(2a-1)$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n8{{x}^{3}}y-2x{{y}^{3}} &amp; = &amp; 2xy(4{{x}^{2}}-{{y}^{2}})\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2xy(2x+y)(2x-y)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n2{{x}^{2}}+12x+18 &amp; = &amp; 2({{x}^{2}}+6x+9)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2{{(x+3)}^{2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2(x+3)(x+3)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n3{{a}^{2}}x+6ax+3x &amp; = &amp; 3x({{a}^{2}}+2a+1)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 3x{{(a+1)}^{2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 3x(a+1)(a+1)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n{{x}^{3}}-x &amp; = &amp; x({{x}^{2}}-1)\u00a0 \\\\<br \/>\n{} &amp; = &amp; x(x+1)(x-1)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n{{a}^{2}}(a-2)-2a(a-2)+(a-2) &amp; = &amp; (a-2)({{a}^{2}}-2a+1)\u00a0 \\\\<br \/>\n{} &amp; = &amp; (a-2){{(a-1)}^{2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; (a-2)(a-1)(a-1)\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<\/ol>\n<div id=\"_mcePaste\" class=\"mcePaste\" style=\"position: absolute; width: 1px; height: 1px; overflow: hidden; top: 0px; left: -10000px;\"><\/div>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6899' onClick='GTTabs_show(0,6899)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Decomp\u00f5e em fatores os polin\u00f3mios: ${{x}^{2}}-6x+9$ $4{{x}^{2}}+4x+1$ ${{a}^{2}}+2ab+{{b}^{2}}$ ${{y}^{2}}-25$ $4{{a}^{2}}-1$ $8{{x}^{3}}y-2x{{y}^{3}}$ $2{{x}^{2}}+12x+18$ $3{{a}^{2}}x+6ax+3x$ ${{x}^{3}}-x$ ${{a}^{2}}(a-2)-2a(a-2)+(a-2)$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14057,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,193],"tags":[197],"series":[],"class_list":["post-6899","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-de-grau-superior-ao-1-","tag-decomposicao-em-factores"],"views":12984,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat02.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6899","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6899"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6899\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14057"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6899"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6899"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6899"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}