{"id":24737,"date":"2023-04-02T16:38:28","date_gmt":"2023-04-02T15:38:28","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24737"},"modified":"2023-04-02T17:15:20","modified_gmt":"2023-04-02T16:15:20","slug":"considera-os-seguintes-polinomios-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24737","title":{"rendered":"Considera os seguintes polin\u00f3mios"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24737' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24737' class='GTTabs_curr'><a  id=\"24737_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24737' ><a  id=\"24737_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_24737'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera os seguintes polin\u00f3mios.<\/p>\n<p style=\"text-align: center;\">\\(A = 2{x^2} &#8211; x &#8211; 1\\)\u00a0 \u00a0 \u00a0 \u00a0 \\(B = &#8211; 3{x^2} + 3x\\)\u00a0 \u00a0 \u00a0 \u00a0 \\(C = 4{x^3} &#8211; 3\\)\u00a0 \u00a0 \u00a0 \u00a0\\(D = 2x + 6\\)<\/p>\n<ol>\n<li>Qual \u00e9 o grau de cada um dos polin\u00f3mios?<\/li>\n<li>Calcula e, em cada caso, apresenta na forma reduzida, o polin\u00f3mio obtido.<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\(A + B\\)<\/li>\n<li>\\(A + C + D\\)<\/li>\n<li>\\(2B &#8211; 3D\\)<\/li>\n<li>\\(C \\times D\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24737' onClick='GTTabs_show(1,24737)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24737'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Considera os seguintes polin\u00f3mios.<\/p>\n<\/blockquote>\n<p style=\"text-align: center;\">\\(A = 2{x^2} &#8211; x &#8211; 1\\)\u00a0 \u00a0 \u00a0 \u00a0 \\(B = &#8211; 3{x^2} + 3x\\)\u00a0 \u00a0 \u00a0 \u00a0 \\(C = 4{x^3} &#8211; 3\\)\u00a0 \u00a0 \u00a0 \u00a0\\(D = 2x + 6\\)<\/p>\n<ol>\n<li>O polin\u00f3mio A tem grau 2.<br \/>O polin\u00f3mio B tem grau 2.<br \/>O polin\u00f3mio C tem grau 3.<br \/>O polin\u00f3mio D tem grau 1.<br \/><br \/><\/li>\n<li>Em cada caso, na forma reduzida, o polin\u00f3mio obtido \u00e9:<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><br \/>\\[\\begin{array}{*{20}{l}}{A + B}&amp; = &amp;{\\left( {2{x^2} &#8211; x &#8211; 1} \\right) + \\left( { &#8211; 3{x^2} + 3x} \\right)}\\\\{}&amp; = &amp;{2{x^2} &#8211; x &#8211; 1 &#8211; 3{x^2} + 3x}\\\\{}&amp; = &amp;{ &#8211; {x^2} + 2x &#8211; 1}\\end{array}\\]<\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{A + C + D}&amp; = &amp;{\\left( {2{x^2} &#8211; x &#8211; 1} \\right) + \\left( {4{x^3} &#8211; 3} \\right) + \\left( {2x + 6} \\right)}\\\\{}&amp; = &amp;{2{x^2} &#8211; x &#8211; 1 + 4{x^3} &#8211; 3 + 2x + 6}\\\\{}&amp; = &amp;{4{x^3} + 2{x^2} + x + 2}\\end{array}\\]<\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{2B &#8211; 3D}&amp; = &amp;{2\\left( { &#8211; 3{x^2} + 3x} \\right) &#8211; 3\\left( {2x + 6} \\right)}\\\\{}&amp; = &amp;{ &#8211; 6{x^2} + 6x &#8211; 6x &#8211; 18}\\\\{}&amp; = &amp;{ &#8211; 6{x^2} &#8211; 18}\\end{array}\\]<\/li>\n<li><br \/>\\[\\begin{array}{*{20}{l}}{C \\times D}&amp; = &amp;{\\left( {4{x^3} &#8211; 3} \\right) \\times \\left( {2x + 6} \\right)}\\\\{}&amp; = &amp;{8{x^4} + 24{x^3} &#8211; 6x &#8211; 18}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24737' onClick='GTTabs_show(0,24737)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera os seguintes polin\u00f3mios. \\(A = 2{x^2} &#8211; x &#8211; 1\\)\u00a0 \u00a0 \u00a0 \u00a0 \\(B = &#8211; 3{x^2} + 3x\\)\u00a0 \u00a0 \u00a0 \u00a0 \\(C = 4{x^3} &#8211; 3\\)\u00a0 \u00a0 \u00a0 \u00a0\\(D&#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":[424,195,705],"series":[],"class_list":["post-24737","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-operacoes-com-polinomios","tag-polinomios"],"views":93,"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\/24737","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=24737"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24737\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24737"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24737"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24737"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24737"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}