{"id":24764,"date":"2023-04-03T10:56:27","date_gmt":"2023-04-03T09:56:27","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24764"},"modified":"2023-04-03T11:29:58","modified_gmt":"2023-04-03T10:29:58","slug":"fatorizacao-de-polinomios","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24764","title":{"rendered":"Fatoriza\u00e7\u00e3o de polin\u00f3mios"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24764' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24764' class='GTTabs_curr'><a  id=\"24764_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24764' ><a  id=\"24764_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_24764'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Associa a cada um dos seguintes polin\u00f3mios a sua fatoriza\u00e7\u00e3o.<\/p>\n<table class=\" aligncenter\" style=\"width: 80%; border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"width: 16.6667%;\">\\(4{x^2} + 12x + 9\\)<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0A\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\u00a0<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a01\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\\({\\left( {3x &#8211; 2} \\right)^2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 16.6667%;\">\\({x^2} &#8211; 16\\)<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0B\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\u00a0<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a02\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\\({\\left( {2x + 3} \\right)^2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 16.6667%;\">\\(9{x^2} &#8211; 12x + 4\\)<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0C\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\u00a0<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a03\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\\(\\left( {4x &#8211; 1} \\right)\\left( {4x + 1} \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 16.6667%;\">\\(4{x^2} &#8211; 1\\)<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0D\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\u00a0<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a04\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\\(\\left( {x + 4} \\right)\\left( {x &#8211; 4} \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 16.6667%;\">\\(4{x^2} &#8211; 12x + 9\\)<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0E\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\u00a0<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a05\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\\(\\left( {2x &#8211; 1} \\right)\\left( {2x + 1} \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 16.6667%;\">\\(16{x^2} &#8211; 1\\)<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0F\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\u00a0<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a06\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\\({\\left( {2x &#8211; 3} \\right)^2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 16.6667%;\">\\(9{x^2} + 12x + 4\\)<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0G\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\u00a0<\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a07\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%;\">\\({\\left( {3x + 2} \\right)^2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24764' onClick='GTTabs_show(1,24764)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24764'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>A associa\u00e7\u00e3o entre cada um dos polin\u00f3mios e a sua fatoriza\u00e7\u00e3o est\u00e1 indicada abaixo.<\/p>\n<table class=\" aligncenter\" style=\"width: 80%; border-collapse: collapse; height: 350px;\">\n<tbody>\n<tr style=\"height: 41px;\">\n<td style=\"width: 16.6667%; height: 41px;\">\\(4{x^2} + 12x + 9\\)<\/td>\n<td style=\"width: 16.6667%; height: 41px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0A\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 41px;\">\u00a0<\/td>\n<td style=\"width: 16.6667%; height: 41px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a01\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 41px;\">\\({\\left( {3x &#8211; 2} \\right)^2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 41px;\">\n<td style=\"width: 16.6667%; height: 41px;\">\\({x^2} &#8211; 16\\)<\/td>\n<td style=\"width: 16.6667%; height: 41px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0B\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 41px;\">\u00a0<\/td>\n<td style=\"width: 16.6667%; height: 41px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a02\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 41px;\">\\({\\left( {2x + 3} \\right)^2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 16.6667%; height: 62px;\">\\(9{x^2} &#8211; 12x + 4\\)<\/td>\n<td style=\"width: 16.6667%; height: 62px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0C\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 62px;\">\u00a0<\/td>\n<td style=\"width: 16.6667%; height: 62px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a03\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 62px;\">\\(\\left( {4x &#8211; 1} \\right)\\left( {4x + 1} \\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 16.6667%; height: 62px;\">\\(4{x^2} &#8211; 1\\)<\/td>\n<td style=\"width: 16.6667%; height: 62px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0D\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 62px;\">\u00a0<\/td>\n<td style=\"width: 16.6667%; height: 62px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a04\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 62px;\">\\(\\left( {x + 4} \\right)\\left( {x &#8211; 4} \\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 16.6667%; height: 62px;\">\\(4{x^2} &#8211; 12x + 9\\)<\/td>\n<td style=\"width: 16.6667%; height: 62px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0E\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 62px;\">\u00a0<\/td>\n<td style=\"width: 16.6667%; height: 62px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a05\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 62px;\">\\(\\left( {2x &#8211; 1} \\right)\\left( {2x + 1} \\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 41px;\">\n<td style=\"width: 16.6667%; height: 41px;\">\\(16{x^2} &#8211; 1\\)<\/td>\n<td style=\"width: 16.6667%; height: 41px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0F\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 41px;\">\u00a0<\/td>\n<td style=\"width: 16.6667%; height: 41px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a06\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 41px;\">\\({\\left( {2x &#8211; 3} \\right)^2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 41px;\">\n<td style=\"width: 16.6667%; height: 41px;\">\\(9{x^2} + 12x + 4\\)<\/td>\n<td style=\"width: 16.6667%; height: 41px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0G\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 41px;\">\u00a0<\/td>\n<td style=\"width: 16.6667%; height: 41px;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a07\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 16.6667%; height: 41px;\">\\({\\left( {3x + 2} \\right)^2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<table class=\" aligncenter\" style=\"width: 80%; border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0A\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0B\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0C\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0D\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0E\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0F\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a0G\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a02\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a04\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a01\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a05\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a06\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a03\u00a0<\/span><\/strong><\/span><\/td>\n<td style=\"width: 14.2857%;\"><span style=\"color: #ffffff;\"><strong><span style=\"background-color: #008000;\">\u00a07\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24764' onClick='GTTabs_show(0,24764)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Associa a cada um dos seguintes polin\u00f3mios a sua fatoriza\u00e7\u00e3o. \\(4{x^2} + 12x + 9\\) \u00a0A\u00a0 \u00a0 \u00a01\u00a0 \\({\\left( {3x &#8211; 2} \\right)^2}\\) \\({x^2} &#8211; 16\\) \u00a0B\u00a0 \u00a0 \u00a02\u00a0 \\({\\left( {2x&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19188,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,197,705],"series":[],"class_list":["post-24764","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-monomios-e-polinomios","tag-8-o-ano","tag-decomposicao-em-factores","tag-polinomios"],"views":116,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat74.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24764","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=24764"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24764\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19188"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24764"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24764"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24764"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}