{"id":6900,"date":"2011-06-06T23:54:17","date_gmt":"2011-06-06T22:54:17","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6900"},"modified":"2022-01-18T21:13:09","modified_gmt":"2022-01-18T21:13:09","slug":"sera-possivel-factorizar-o-trinomio-4x210x9","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6900","title":{"rendered":"Ser\u00e1 poss\u00edvel fatorizar o trin\u00f3mio $4{{x}^{2}}+10x+9$ ?"},"content":{"rendered":"<p><ul id='GTTabs_ul_6900' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6900' class='GTTabs_curr'><a  id=\"6900_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6900' ><a  id=\"6900_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_6900'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Ser\u00e1 poss\u00edvel fatorizar o trin\u00f3mio $4{{x}^{2}}+10x+9$ ?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6900' onClick='GTTabs_show(1,6900)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6900'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Ora,<\/p>\n<p>\\[\\begin{array}{*{35}{l}} \u00a0\u00a0 4{{x}^{2}}+10x+9 &amp; = &amp; 4{{x}^{2}}+10x+{{\\left( \\frac{5}{2} \\right)}^{2}}-{{\\left( \\frac{5}{2} \\right)}^{2}}+9\u00a0 \\\\ \u00a0\u00a0 {} &amp; = &amp; {{\\left( 2x+\\frac{5}{2} \\right)}^{2}}-\\frac{25}{4}+\\underset{(4)}{\\mathop{9}}\\,\u00a0 \\\\ \u00a0\u00a0 {} &amp; = &amp; {{\\left( 2x+\\frac{5}{2} \\right)}^{2}}-\\frac{25}{4}+\\frac{36}{4}\u00a0 \\\\ \u00a0\u00a0 {} &amp; = &amp; {{\\left( 2x+\\frac{5}{2} \\right)}^{2}}+\\frac{11}{4}\u00a0 \\\\ \\end{array}\\]<\/p>\n<p>Como ${{\\left( 2x+\\frac{5}{2} \\right)}^{2}}\\ge 0$, ent\u00e3o ${{\\left( 2x+\\frac{5}{2} \\right)}^{2}}+\\frac{11}{4}&gt;0$.<\/p>\n<p>Portanto, n\u00e3o \u00e9 poss\u00edvel fatorizar o trin\u00f3mio, pois ele n\u00e3o anula, visto n\u00e3o poder ser escrito como uma diferen\u00e7a de quadrados.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6900' onClick='GTTabs_show(0,6900)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Ser\u00e1 poss\u00edvel fatorizar o trin\u00f3mio $4{{x}^{2}}+10x+9$ ? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20603,"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-6900","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":2680,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/06\/8V2Pag075-21_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6900","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=6900"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6900\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20603"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6900"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}