{"id":6876,"date":"2011-05-22T16:27:59","date_gmt":"2011-05-22T15:27:59","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6876"},"modified":"2022-01-05T14:58:27","modified_gmt":"2022-01-05T14:58:27","slug":"determina-e-indica-o-grau-de-cada-polinomio-obtido","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6876","title":{"rendered":"Determina e indica o grau de cada polin\u00f3mio obtido"},"content":{"rendered":"<p><ul id='GTTabs_ul_6876' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6876' class='GTTabs_curr'><a  id=\"6876_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6876' ><a  id=\"6876_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_6876'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera os polin\u00f3mios:<\/p>\n<table class=\"aligncenter\" style=\"width: 70%;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<tbody>\n<tr>\n<td>$A=7{{x}^{2}}-2x+\\frac{1}{2}$<\/td>\n<td>$B={{x}^{2}}-4x$<\/td>\n<td>$C=3{{x}^{2}}-4x+\\frac{7}{3}$<\/td>\n<td>$D=3{{x}^{2}}+\\frac{1}{2}x-\\frac{2}{3}$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Determina e indica o grau de cada polin\u00f3mio obtido:<\/p>\n<ol>\n<li>$A+B$<\/li>\n<li>$B-C$<\/li>\n<li>$C-D$<\/li>\n<li>$A-(B+C+D)$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6876' onClick='GTTabs_show(1,6876)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6876'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table class=\"aligncenter\" style=\"width: 70%;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<tbody>\n<tr>\n<td>$A=7{{x}^{2}}-2x+\\frac{1}{2}$<\/td>\n<td>$B={{x}^{2}}-4x$<\/td>\n<td>$C=3{{x}^{2}}-4x+\\frac{7}{3}$<\/td>\n<td>$D=3{{x}^{2}}+\\frac{1}{2}x-\\frac{2}{3}$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nA+B &amp; = &amp; (7{{x}^{2}}-2x+\\frac{1}{2})+({{x}^{2}}-4x)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 7{{x}^{2}}+{{x}^{2}}-2x-4x+\\frac{1}{2}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 8{{x}^{2}}-6x+\\frac{1}{2}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nO polin\u00f3mio obtido \u00e9 de grau 2.<br \/>\n\u00ad<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nB-C &amp; = &amp; ({{x}^{2}}-4x)-(3{{x}^{2}}-4x+\\frac{7}{3})\u00a0 \\\\<br \/>\n{} &amp; = &amp; {{x}^{2}}-4x-3{{x}^{2}}+4x-\\frac{7}{3}\u00a0 \\\\<br \/>\n{} &amp; = &amp; {{x}^{2}}-3{{x}^{2}}-4x+4x-\\frac{7}{3}\u00a0 \\\\<br \/>\n{} &amp; = &amp; -2{{x}^{2}}-\\frac{7}{3}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nO polin\u00f3mio obtido \u00e9 de grau 2.<br \/>\n\u00ad<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nC-D &amp; = &amp; (3{{x}^{2}}-4x+\\frac{7}{3})-(3{{x}^{2}}+\\frac{1}{2}x-\\frac{2}{3})\u00a0 \\\\<br \/>\n{} &amp; = &amp; 3{{x}^{2}}-4x+\\frac{7}{3}-3{{x}^{2}}-\\frac{1}{2}x+\\frac{2}{3}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 3{{x}^{2}}-3{{x}^{2}}-\\underset{(2)}{\\mathop{4x}}\\,-\\frac{1}{\\underset{(1)}{\\mathop{2}}\\,}x+\\frac{7}{3}+\\frac{2}{3}\u00a0 \\\\<br \/>\n{} &amp; = &amp; -\\frac{8}{2}x-\\frac{1}{2}x+\\frac{9}{3}\u00a0 \\\\<br \/>\n{} &amp; = &amp; -\\frac{9}{2}x+3\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nO polin\u00f3mio obtido \u00e9 de grau 1.<br \/>\n\u00ad<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nA-(B+C+D) &amp; = &amp; (7{{x}^{2}}-2x+\\frac{1}{2})-\\left[ ({{x}^{2}}-4x)+(3{{x}^{2}}-4x+\\frac{7}{3})+(3{{x}^{2}}+\\frac{1}{2}x-\\frac{2}{3}) \\right]\u00a0 \\\\<br \/>\n{} &amp; = &amp; (7{{x}^{2}}-2x+\\frac{1}{2})-({{x}^{2}}-4x+3{{x}^{2}}-4x+\\frac{7}{3}+3{{x}^{2}}+\\frac{1}{2}x-\\frac{2}{3})\u00a0 \\\\<br \/>\n{} &amp; = &amp; (7{{x}^{2}}-2x+\\frac{1}{2})-({{x}^{2}}+3{{x}^{2}}+3{{x}^{2}}-\\underset{(2)}{\\mathop{4x}}\\,-\\underset{(2)}{\\mathop{4x}}\\,+\\frac{1}{\\underset{(1)}{\\mathop{2}}\\,}x+\\frac{7}{3}-\\frac{2}{3})\u00a0 \\\\<br \/>\n{} &amp; = &amp; (7{{x}^{2}}-2x+\\frac{1}{2})-(7{{x}^{2}}-\\frac{15}{2}x+\\frac{5}{3})\u00a0 \\\\<br \/>\n{} &amp; = &amp; 7{{x}^{2}}-2x+\\frac{1}{2}-7{{x}^{2}}+\\frac{15}{2}x-\\frac{5}{3}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 7{{x}^{2}}-7{{x}^{2}}-\\underset{(2)}{\\mathop{2x}}\\,+\\frac{15}{\\underset{(1)}{\\mathop{2}}\\,}x+\\frac{1}{\\underset{(3)}{\\mathop{2}}\\,}-\\frac{5}{\\underset{(2)}{\\mathop{3}}\\,}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{11}{2}x-\\frac{7}{6}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\n<strong>Alternativa<\/strong>:<br \/>\nPara evitar reduzir os termos semelhantes por duas vezes, ser\u00e1 prefer\u00edvel come\u00e7ar por desembara\u00e7ar os par\u00eantesis:<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nA-(B+C+D) &amp; = &amp; (7{{x}^{2}}-2x+\\frac{1}{2})-\\left[ ({{x}^{2}}-4x)+(3{{x}^{2}}-4x+\\frac{7}{3})+(3{{x}^{2}}+\\frac{1}{2}x-\\frac{2}{3}) \\right]\u00a0 \\\\<br \/>\n{} &amp; = &amp; 7{{x}^{2}}-2x+\\frac{1}{2}-{{x}^{2}}+4x-3{{x}^{2}}+4x-\\frac{7}{3}-3{{x}^{2}}-\\frac{1}{2}x+\\frac{2}{3}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 7{{x}^{2}}-{{x}^{2}}-3{{x}^{2}}-3{{x}^{2}}-2x+4x+4x-\\frac{1}{2}x+\\frac{1}{2}-\\frac{7}{3}+\\frac{2}{3}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\underset{(2)}{\\mathop{6x}}\\,-\\frac{1}{\\underset{(1)}{\\mathop{2}}\\,}x+\\frac{1}{\\underset{(3)}{\\mathop{2}}\\,}-\\frac{5}{\\underset{(2)}{\\mathop{3}}\\,}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{11}{2}x-\\frac{7}{6}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nO polin\u00f3mio obtido \u00e9 de grau 1.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6876' onClick='GTTabs_show(0,6876)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera os polin\u00f3mios: $A=7{{x}^{2}}-2x+\\frac{1}{2}$ $B={{x}^{2}}-4x$ $C=3{{x}^{2}}-4x+\\frac{7}{3}$ $D=3{{x}^{2}}+\\frac{1}{2}x-\\frac{2}{3}$ Determina e indica o grau de cada polin\u00f3mio obtido: $A+B$ $B-C$ $C-D$ $A-(B+C+D)$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,193],"tags":[195],"series":[],"class_list":["post-6876","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-de-grau-superior-ao-1-","tag-operacoes-com-polinomios"],"views":1496,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6876","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=6876"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6876\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14083"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6876"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6876"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6876"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}