{"id":24481,"date":"2023-02-17T11:53:41","date_gmt":"2023-02-17T11:53:41","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24481"},"modified":"2023-02-17T15:22:54","modified_gmt":"2023-02-17T15:22:54","slug":"considera-os-seguintes-polinomios","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24481","title":{"rendered":"Considera os seguintes polin\u00f3mios"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24481' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24481' class='GTTabs_curr'><a  id=\"24481_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24481' ><a  id=\"24481_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_24481'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera os seguintes polin\u00f3mios, onde <em>x<\/em> e <em>y<\/em> s\u00e3o vari\u00e1veis e <em>a<\/em> e <em>b<\/em> s\u00e3o constantes.<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td><strong>(A)<\/strong><\/td>\n<td style=\"text-align: left;\">\\( &#8211; 4{x^3} + 10 + 7{x^2} &#8211; {x^3} &#8211; 11 + 5{x^3}\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>(B)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(3xy &#8211; 7{x^2}{y^2} &#8211; \\frac{2}{3}xy + \\frac{{{x^2}{y^2}}}{5} + 37\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>(C)<\/strong><\/td>\n<td style=\"text-align: left;\">\\(7a{x^2} + bx &#8211; 5a{x^2} + 7{x^2} &#8211; 1 &#8211; 2a{x^2} &#8211; bx\\)<\/td>\n<\/tr>\n<tr>\n<td><strong>(D)<\/strong><\/td>\n<td style=\"text-align: left;\">\\({x^2}y + \\frac{1}{5}xy &#8211; \\frac{7}{4}xy + 2{x^2}y &#8211; \\frac{{xy}}{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Identifica as vari\u00e1veis de cada um dos polin\u00f3mios.<\/li>\n<li>Escreve uma forma reduzida de cada um dos polin\u00f3mios.<\/li>\n<li>Indica o grau de cada um dos polin\u00f3mios.<\/li>\n<li>Identifica dois polin\u00f3mios iguais.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24481' onClick='GTTabs_show(1,24481)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24481'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Nos polin\u00f3mios seguintes, <em>x<\/em> e <em>y<\/em> s\u00e3o vari\u00e1veis e <em>a<\/em> e <em>b<\/em> s\u00e3o constantes.<\/p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td><strong>Polin\u00f3mio \/ Forma reduzida<\/strong><\/td>\n<td><strong>Vari\u00e1veis<\/strong><\/td>\n<td><strong>Grau<\/strong><\/td>\n<td><strong>Polin\u00f3mios iguais<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>(A)<\/strong><\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{ &#8211; 4{x^3} + 10 + 7{x^2} &#8211; {x^3} &#8211; 11 + 5{x^3}}&amp; = &amp;{\\left( { &#8211; 4 &#8211; 1 + 5} \\right){x^3} + 7{x^2} + \\left( {10 &#8211; 11} \\right)}\\\\{}&amp; = &amp;{7{x^2} &#8211; 1}\\end{array}\\]<\/td>\n<td>\\(x\\)<\/td>\n<td>2<\/td>\n<td>X<\/td>\n<\/tr>\n<tr>\n<td><strong>(B)<\/strong><\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{3xy &#8211; 7{x^2}{y^2} &#8211; \\frac{2}{3}xy + \\frac{{{x^2}{y^2}}}{5} + 3}&amp; = &amp;{\\left( { &#8211; 7 + \\frac{1}{5}} \\right){x^2}{y^2} + \\left( {3 &#8211; \\frac{2}{3}} \\right)xy + 3}\\\\{}&amp; = &amp;{ &#8211; \\frac{{34}}{5}{x^2}{y^2} + \\frac{7}{3}xy + 3}\\end{array}\\]<\/td>\n<td>\\(x\\) e \\(y\\)<\/td>\n<td>4<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td><strong>(C)<\/strong><\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{7a{x^2} + bx &#8211; 5a{x^2} + 7{x^2} &#8211; 1 &#8211; 2a{x^2} &#8211; bx}&amp; = &amp;{\\left( {7a &#8211; 5a + 7 &#8211; 2a} \\right){x^2} + \\left( {b &#8211; b} \\right)x &#8211; 1}\\\\{}&amp; = &amp;{7{x^2} &#8211; 1}\\end{array}\\]<\/td>\n<td>\\(x\\)<\/td>\n<td>2<\/td>\n<td>X<\/td>\n<\/tr>\n<tr>\n<td><strong>(D)<\/strong><\/td>\n<td style=\"text-align: left;\">\\[\\begin{array}{*{20}{l}}{{x^2}y + \\frac{1}{5}xy &#8211; \\frac{7}{4}xy + 2{x^2}y &#8211; \\frac{{xy}}{2}}&amp; = &amp;{\\left( {1 + 2} \\right){x^2}y + \\left( {\\frac{1}{{\\mathop 5\\limits_{\\left( 4 \\right)} }} &#8211; \\frac{7}{{\\mathop 4\\limits_{\\left( 5 \\right)} }} &#8211; \\frac{1}{{\\mathop 2\\limits_{\\left( {10} \\right)} }}} \\right)xy}\\\\{}&amp; = &amp;{3{x^2}y &#8211; \\frac{{41}}{{20}}xy}\\end{array}\\]<\/td>\n<td>\\(x\\) e \\(y\\)<\/td>\n<td>3<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24481' onClick='GTTabs_show(0,24481)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera os seguintes polin\u00f3mios, onde x e y s\u00e3o vari\u00e1veis e a e b s\u00e3o constantes. (A) \\( &#8211; 4{x^3} + 10 + 7{x^2} &#8211; {x^3} &#8211; 11 + 5{x^3}\\) (B)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19269,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,705],"series":[],"class_list":["post-24481","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-polinomios"],"views":136,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat90.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24481","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=24481"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24481\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19269"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24481"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24481"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24481"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24481"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}