{"id":24758,"date":"2023-04-02T21:11:22","date_gmt":"2023-04-02T20:11:22","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24758"},"modified":"2023-04-02T21:40:27","modified_gmt":"2023-04-02T20:40:27","slug":"apresenta-os-polinomios-na-forma-reduzida","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24758","title":{"rendered":"Apresenta os polin\u00f3mios na forma reduzida"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24758' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24758' class='GTTabs_curr'><a  id=\"24758_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24758' ><a  id=\"24758_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_24758'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Apresenta cada um dos polin\u00f3mios seguintes na forma reduzida.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 3.125%;\">a)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\(15x &#8211; {\\left( {x + 7} \\right)^2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">b)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\(x\\left( {x &#8211; 1} \\right) &#8211; {\\left( {x &#8211; 2} \\right)^2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">c)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\(\\left( {x + 2} \\right)\\left( {x &#8211; 3} \\right) + {\\left( {x + 1} \\right)^2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">d)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\({\\left( {x + \\frac{1}{2}} \\right)^2} &#8211; {\\left( {x &#8211; \\frac{1}{2}} \\right)^2} &#8211; \\frac{3}{4}\\left( {x &#8211; 1} \\right)\\left( {x + 1} \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">e)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\(2x\\left( {{x^2} + 3x &#8211; \\frac{1}{2}} \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">f)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\(\\left( {n &#8211; 2} \\right)\\left( {n + 3} \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">g)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\(\\left( {1 &#8211; y &#8211; {y^2}} \\right)\\left( {y + 2} \\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">h)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\(\\left( {{t^2} &#8211; t + 1} \\right)\\left( {{t^3} &#8211; 2t + 5} \\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24758' onClick='GTTabs_show(1,24758)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24758'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Apresenta-se abaixo cada um dos polin\u00f3mios na forma reduzida.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 3.125%;\">a)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\[\\begin{array}{*{20}{l}}{15x &#8211; {{\\left( {x + 7} \\right)}^2}}&amp; = &amp;{15x &#8211; \\left( {{x^2} + 14x + 49} \\right)}\\\\{}&amp; = &amp;{ &#8211; {x^2} + x &#8211; 49}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">b)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\[\\begin{array}{*{20}{l}}{x\\left( {x &#8211; 1} \\right) &#8211; {{\\left( {x &#8211; 2} \\right)}^2}}&amp; = &amp;{{x^2} &#8211; x &#8211; \\left( {{x^2} &#8211; 4x + 4} \\right)}\\\\{}&amp; = &amp;{3x &#8211; 4}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">c)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\[\\begin{array}{*{20}{l}}{\\left( {x + 2} \\right)\\left( {x &#8211; 3} \\right) + {{\\left( {x + 1} \\right)}^2}}&amp; = &amp;{{x^2} &#8211; 3x + 2x &#8211; 6 + \\left( {{x^2} + 2x + 1} \\right)}\\\\{}&amp; = &amp;{2{x^2} + x &#8211; 5}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">d)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\[\\begin{array}{*{20}{l}}{{{\\left( {x + \\frac{1}{2}} \\right)}^2} &#8211; {{\\left( {x &#8211; \\frac{1}{2}} \\right)}^2} &#8211; \\frac{3}{4}\\left( {x &#8211; 1} \\right)\\left( {x + 1} \\right)}&amp; = &amp;{\\left( {x + \\frac{1}{2} + x &#8211; \\frac{1}{2}} \\right)\\left( {x + \\frac{1}{2} &#8211; x + \\frac{1}{2}} \\right) &#8211; \\frac{3}{4}\\left( {{x^2} &#8211; 1} \\right)}\\\\{}&amp; = &amp;{2x \\times 1 &#8211; \\frac{3}{4}{x^2} + \\frac{3}{4}}\\\\{}&amp; = &amp;{ &#8211; \\frac{3}{4}{x^2} + 2x + \\frac{3}{4}}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">e)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\[\\begin{array}{*{20}{l}}{2x\\left( {{x^2} + 3x &#8211; \\frac{1}{2}} \\right)}&amp; = &amp;{2{x^3} + 6{x^2} &#8211; x}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">f)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\[\\begin{array}{*{20}{l}}{\\left( {n &#8211; 2} \\right)\\left( {n + 3} \\right)}&amp; = &amp;{{n^2} + 3n &#8211; 2n &#8211; 6}\\\\{}&amp; = &amp;{{n^2} + n &#8211; 6}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">g)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\[\\begin{array}{*{20}{l}}{\\left( {1 &#8211; y &#8211; {y^2}} \\right)\\left( {y + 2} \\right)}&amp; = &amp;{y + 2 &#8211; {y^2} &#8211; 2y &#8211; {y^3} &#8211; 2{y^2}}\\\\{}&amp; = &amp;{ &#8211; {y^3} &#8211; 3{y^2} &#8211; y + 2}\\end{array}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">h)<\/td>\n<td style=\"text-align: left; width: 96.7447%;\">\\[\\begin{array}{*{20}{l}}{\\left( {{t^2} &#8211; t + 1} \\right)\\left( {{t^3} &#8211; 2t + 5} \\right)}&amp; = &amp;{{t^5} &#8211; 2{t^3} + 5{t^2} &#8211; {t^4} + 2{t^2} &#8211; 5t + {t^3} &#8211; 2t + 5}\\\\{}&amp; = &amp;{{t^5} &#8211; {t^4} &#8211; {t^3} + 7{t^2} &#8211; 7t + 5}\\end{array}\\]<\/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_24758' onClick='GTTabs_show(0,24758)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Apresenta cada um dos polin\u00f3mios seguintes na forma reduzida. a) \\(15x &#8211; {\\left( {x + 7} \\right)^2}\\) b) \\(x\\left( {x &#8211; 1} \\right) &#8211; {\\left( {x &#8211; 2} \\right)^2}\\) c) \\(\\left(&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19189,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,196,195,705],"series":[],"class_list":["post-24758","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-casos-notaveis","tag-operacoes-com-polinomios","tag-polinomios"],"views":97,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat75.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24758","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=24758"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24758\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19189"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24758"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24758"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24758"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24758"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}