{"id":24508,"date":"2023-02-22T22:13:54","date_gmt":"2023-02-22T22:13:54","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24508"},"modified":"2023-02-22T22:45:23","modified_gmt":"2023-02-22T22:45:23","slug":"considera-os-polinomios-ab-c-e-d","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24508","title":{"rendered":"Considera os polin\u00f3mios A, B, C e D"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24508' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24508' class='GTTabs_curr'><a  id=\"24508_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24508' ><a  id=\"24508_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_24508'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera os polin\u00f3mios A, B, C e D.<\/p>\n<p>\\(A = 7{x^2} &#8211; 2x + \\frac{1}{2}\\)<\/p>\n<p>\\(B = {x^2} &#8211; 4x\\)<\/p>\n<p>\\(C = 3{x^2} &#8211; 4x + \\frac{7}{3}\\)<\/p>\n<p>\\(D = 3{x^2} + \\frac{1}{2}x &#8211; \\frac{2}{3}\\)<\/p>\n<p>Determina, apresentando o resultado na forma de um polin\u00f3mio reduzido e ordenado, e indica o grau desse polin\u00f3mio:<\/p>\n<ol>\n<li>\\(A + B\\)<\/li>\n<li>\\(B &#8211; C\\)<\/li>\n<li>\\(C &#8211; D\\)<\/li>\n<li>\\(A &#8211; \\left( {B + C + D} \\right)\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24508' onClick='GTTabs_show(1,24508)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24508'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Considera os polin\u00f3mios A, B, C e D.<\/p>\n<p>\\(A = 7{x^2} &#8211; 2x + \\frac{1}{2}\\)<\/p>\n<p>\\(B = {x^2} &#8211; 4x\\)<\/p>\n<p>\\(C = 3{x^2} &#8211; 4x + \\frac{7}{3}\\)<\/p>\n<p>\\(D = 3{x^2} + \\frac{1}{2}x &#8211; \\frac{2}{3}\\)<\/p>\n<p>Determina, apresentando o resultado na forma de um polin\u00f3mio reduzido e ordenado, e indica o grau desse polin\u00f3mio:<\/p>\n<\/blockquote>\n<ol>\n<li>\\(A + B\\)<br \/>\\[\\begin{array}{*{20}{l}}{A + B}&amp; = &amp;{\\left( {7{x^2} &#8211; 2x + \\frac{1}{2}} \\right) + \\left( {{x^2} &#8211; 4x} \\right)}\\\\{}&amp; = &amp;{8{x^2} &#8211; 6x + \\frac{1}{2}}\\end{array}\\]<br \/>O polin\u00f3mio \u00e9 de grau 2.<br \/><br \/><\/li>\n<li>\\(B &#8211; C\\)<br \/>\\[\\begin{array}{*{20}{l}}{B &#8211; C}&amp; = &amp;{\\left( {{x^2} &#8211; 4x} \\right) &#8211; \\left( {3{x^2} &#8211; 4x + \\frac{7}{3}} \\right)}\\\\{}&amp; = &amp;{ &#8211; 2{x^2} &#8211; \\frac{7}{3}}\\end{array}\\]<br \/>O polin\u00f3mio \u00e9 de grau 2.<br \/><br \/><\/li>\n<li>\\(C &#8211; D\\)<br \/>\\[\\begin{array}{*{20}{l}}{C &#8211; D}&amp; = &amp;{\\left( {3{x^2} &#8211; \\mathop 4\\limits_{\\left( 2 \\right)} x + \\frac{7}{3}} \\right) &#8211; \\left( {3{x^2} + \\frac{1}{2}x &#8211; \\frac{2}{3}} \\right)}\\\\{}&amp; = &amp;{ &#8211; \\frac{9}{2}x + 3}\\end{array}\\]<br \/>O polin\u00f3mio \u00e9 de grau 1.<br \/><br \/><\/li>\n<li>\\(A &#8211; \\left( {B + C + D} \\right)\\)<br \/>\\[\\begin{array}{*{20}{l}}{A &#8211; \\left( {B + C + D} \\right)}&amp; = &amp;{\\left( {7{x^2} &#8211; 2x + \\frac{1}{2}} \\right) &#8211; \\left[ {\\left( {{x^2} &#8211; 4x} \\right) + \\left( {3{x^2} &#8211; 4x + \\frac{7}{3}} \\right) + \\left( {3{x^2} + \\frac{1}{2}x &#8211; \\frac{2}{3}} \\right)} \\right]}\\\\{}&amp; = &amp;{\\left( {7{x^2} &#8211; 2x + \\frac{1}{{\\mathop 2\\limits_{\\left( 3 \\right)} }}} \\right) &#8211; \\left( {7{x^2} &#8211; \\frac{{15}}{2}x + \\frac{5}{{\\mathop 3\\limits_{\\left( 2 \\right)} }}} \\right)}\\\\{}&amp; = &amp;{\\frac{{11}}{2}x &#8211; \\frac{7}{6}}\\end{array}\\]<br \/>O polin\u00f3mio \u00e9 de grau 1.<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24508' onClick='GTTabs_show(0,24508)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera os polin\u00f3mios A, B, C e D. \\(A = 7{x^2} &#8211; 2x + \\frac{1}{2}\\) \\(B = {x^2} &#8211; 4x\\) \\(C = 3{x^2} &#8211; 4x + \\frac{7}{3}\\) \\(D = 3{x^2} +&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19178,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,194,195,705],"series":[],"class_list":["post-24508","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-monomios","tag-operacoes-com-polinomios","tag-polinomios"],"views":287,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat69.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24508","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=24508"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24508\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19178"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24508"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24508"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24508"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}