{"id":6885,"date":"2011-05-24T22:31:43","date_gmt":"2011-05-24T21:31:43","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6885"},"modified":"2022-01-05T15:19:45","modified_gmt":"2022-01-05T15:19:45","slug":"dados-os-polinomios","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6885","title":{"rendered":"Dados os polin\u00f3mios"},"content":{"rendered":"<p><ul id='GTTabs_ul_6885' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6885' class='GTTabs_curr'><a  id=\"6885_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6885' ><a  id=\"6885_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_6885'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Dados os polin\u00f3mios:<\/p>\n<table style=\"width: 70%;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$A=2{{x}^{2}}-x-1$<\/td>\n<td style=\"text-align: center;\">$B=-3{{x}^{2}}+3x$<\/td>\n<td style=\"text-align: center;\">$C=4{{x}^{3}}-3$<\/td>\n<td style=\"text-align: center;\">$D=2x+6$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Qual \u00e9 o grau de cada um dos polin\u00f3mios?<\/li>\n<li>Calcula, reduzindo os termos semelhantes:<\/li>\n<\/ol>\n<ul>\n<li>$A+B$<\/li>\n<li>$A+C+D$<\/li>\n<li>$2B-3D$<\/li>\n<li>$C\\times D$<\/li>\n<\/ul>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6885' onClick='GTTabs_show(1,6885)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6885'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table style=\"width: 70%;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$A=2{{x}^{2}}-x-1$<\/td>\n<td style=\"text-align: center;\">$B=-3{{x}^{2}}+3x$<\/td>\n<td style=\"text-align: center;\">$C=4{{x}^{3}}-3$<\/td>\n<td style=\"text-align: center;\">$D=2x+6$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Os polin\u00f3mios A e B s\u00e3o de grau 2, o polin\u00f3mio C \u00e9 de grau 3 e o polin\u00f3mio D \u00e9 de grau 1.<br \/>\n\u00ad<\/li>\n<li>Temos, sucessivamente:<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nA+B &amp; = &amp; (2{{x}^{2}}-x-1)+(-3{{x}^{2}}+3x)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2{{x}^{2}}-x-1-3{{x}^{2}}+3x\u00a0 \\\\<br \/>\n{} &amp; = &amp; -{{x}^{2}}+2x-1\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\nA+C+D &amp; = &amp; (2{{x}^{2}}-x-1)+(4{{x}^{3}}-3)+(2x+6)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2{{x}^{2}}-x-1+4{{x}^{3}}-3+2x+6\u00a0 \\\\<br \/>\n{} &amp; = &amp; 4{{x}^{3}}+2{{x}^{2}}+x+2\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\n2B-3D &amp; = &amp; 2\\times (-3{{x}^{2}}+3x)-3\\times (2x+6)\u00a0 \\\\<br \/>\n{} &amp; = &amp; -6{{x}^{2}}+6x-6x-18\u00a0 \\\\<br \/>\n{} &amp; = &amp; -6{{x}^{2}}-18\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\nC\\times D &amp; = &amp; (4{{x}^{3}}-3)\\times (2x+6)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 8{{x}^{4}}+24{{x}^{3}}-6x-18\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6885' onClick='GTTabs_show(0,6885)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Dados os polin\u00f3mios: $A=2{{x}^{2}}-x-1$ $B=-3{{x}^{2}}+3x$ $C=4{{x}^{3}}-3$ $D=2x+6$ Qual \u00e9 o grau de cada um dos polin\u00f3mios? Calcula, reduzindo os termos semelhantes: $A+B$ $A+C+D$ $2B-3D$ $C\\times D$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19177,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[100,97,193],"tags":[195],"series":[],"class_list":["post-6885","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":2639,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat68.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6885","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=6885"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6885\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6885"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6885"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6885"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6885"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}