{"id":301,"date":"2023-07-06T15:21:06","date_gmt":"2023-07-06T15:21:06","guid":{"rendered":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/"},"modified":"2023-07-06T15:21:06","modified_gmt":"2023-07-06T15:21:06","slug":"grau-de-um-polinomio","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/","title":{"rendered":"Grau de um polin\u00f4mio"},"content":{"rendered":"<p>Nesta p\u00e1gina explicamos o que \u00e9 o grau de um polin\u00f4mio (grau absoluto e grau relativo) e como saber qual \u00e9 o grau de um polin\u00f4mio. Voc\u00ea tamb\u00e9m poder\u00e1 ver v\u00e1rios exemplos de como o grau de um polin\u00f4mio \u00e9 determinado e, al\u00e9m disso, descobrir\u00e1 como os polin\u00f4mios s\u00e3o classificados de acordo com seu grau. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-grado-de-un-polinomio\"><\/span> Qual \u00e9 o grau de um polin\u00f4mio?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A defini\u00e7\u00e3o do grau de um polin\u00f4mio \u00e9 a seguinte:<\/p>\n<p> <strong>Em matem\u00e1tica, o grau de um polin\u00f4mio \u00e9 o maior expoente ao qual a vari\u00e1vel polinomial \u00e9 elevada.<\/strong><\/p>\n<p> Por exemplo, o seguinte polin\u00f4mio \u00e9 de grau 5 porque o valor m\u00e1ximo dos expoentes de seus termos \u00e9 5:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7fcca51a02c5abdfd8a12ef79c2785f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = x^5+2x^4+6x^2-3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Embora pare\u00e7a um conceito muito simples, saber identificar o grau de um polin\u00f4mio \u00e9 essencial para poder somar e subtrair polin\u00f4mios corretamente. Descubra porque \u00e9 t\u00e3o importante nos <a href=\"https:\/\/mathority.org\/pt\/soma-de-polinomios-exemplos-adicao-de-exercicios-resolvidos\/\"><strong><span style=\"text-decoration: underline;\">exemplos de adi\u00e7\u00e3o de polin\u00f4mios<\/span><\/strong><\/a> e <a href=\"https:\/\/mathority.org\/pt\/subtracao-de-polinomios-exemplos-exercicios-resolvidos-subtracao\/\"><strong><span style=\"text-decoration: underline;\">exemplos de subtra\u00e7\u00e3o de polin\u00f4mios<\/span><\/strong><\/a> , onde, al\u00e9m disso, voc\u00ea poder\u00e1 praticar com exerc\u00edcios resolvidos esses dois tipos de opera\u00e7\u00f5es com polin\u00f4mios.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-grados-de-polinomios\"><\/span> Exemplos de graus de polin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de sabermos como identificar o grau de um polin\u00f4mio, vejamos outros exemplos para entender seu significado: <a rel=\"noreferrer noopener\" href=\"https:\/\/www.superprof.es\/clases\/matematicas\/espana\/?_src=9&amp;aff=1812\" target=\"_blank\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.superprof.es\/clases\/matematicas\/espana\/?_src=9&amp;aff=1812\" target=\"_blank\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.superprof.es\/clases\/matematicas\/espana\/?_src=9&amp;aff=1812\" target=\"_blank\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.superprof.es\/clases\/matematicas\/espana\/?_src=9&amp;aff=1812\" target=\"_blank\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.superprof.es\/clases\/matematicas\/espana\/?_src=9&amp;aff=1812\" target=\"_blank\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.superprof.es\/clases\/matematicas\/espana\/?_src=9&amp;aff=1812\" target=\"_blank\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.superprof.es\/clases\/matematicas\/espana\/?_src=9&amp;aff=1812\" target=\"_blank\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.superprof.es\/clases\/matematicas\/espana\/?_src=9&amp;aff=1812\" target=\"_blank\"><\/a><\/p>\n<ul>\n<li> Exemplo de um polin\u00f4mio de grau zero:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d1f126168687c7e08f5e42d8a5ff9c4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Exemplo de um polin\u00f4mio de primeiro grau:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-946d2d190b314e9a1e6e11c6351981b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 3x+2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Exemplo de um polin\u00f4mio de segundo grau:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-859b10f44ce6d4268e09824490d20b5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = x^2+7x-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"151\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Exemplo de um polin\u00f4mio de terceiro grau:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fcb451c07206eb39124c0ace7e889841_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 2x^3+5x^2-9\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"167\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Exemplo de um polin\u00f4mio de quarto grau: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d67bd26fe754b92f9197dae15dbe49e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 6x^4+3x^2-7x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFComo-saber-el-grado-de-un-polinomio-con-dos-o-mas-variables\"><\/span> Como saber o grau de um polin\u00f4mio com duas ou mais vari\u00e1veis?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Acabamos de ver como \u00e9 determinado o grau de um polin\u00f4mio univari\u00e1vel, ou seja, com uma \u00fanica vari\u00e1vel. Mas qual \u00e9 o grau de um polin\u00f4mio multivari\u00e1vel?<\/p>\n<p> Na \u00e1lgebra, existem dois tipos de graus polinomiais quando possui mais de uma vari\u00e1vel:<\/p>\n<ul>\n<li> <strong>Grau absoluto<\/strong> : o grau absoluto corresponde ao grau m\u00e1ximo dos mon\u00f4mios que formam o polin\u00f4mio<\/li>\n<li> <strong>Grau relativo<\/strong> : o grau relativo em rela\u00e7\u00e3o a uma determinada vari\u00e1vel corresponde ao maior expoente dessa vari\u00e1vel.<\/li>\n<\/ul>\n<p> Obviamente, para determinar o grau absoluto de um polin\u00f4mio voc\u00ea precisa saber como \u00e9 calculado o grau de um mon\u00f4mio com 2 ou mais vari\u00e1veis, ent\u00e3o se voc\u00ea n\u00e3o se lembra como isso foi feito recomendamos dar uma olhada em nossa p\u00e1gina sobre as <a href=\"https:\/\/mathority.org\/pt\/partes-de-um-coeficiente-monomio-parte-literal-e-grau-variavel\/\"><strong><span style=\"text-decoration: underline;\">partes de um mon\u00f4mio<\/span><\/strong><\/a> . Nesta p\u00e1gina voc\u00ea encontrar\u00e1 uma explica\u00e7\u00e3o de todas as partes de um mon\u00f4mio e, mais especificamente, <span style=\"text-decoration: underline;\">como determinar o grau de um mon\u00f4mio multivari\u00e1vel<\/span> .<\/p>\n<p> Como exemplo, encontraremos os graus absolutos e relativos do seguinte polin\u00f4mio com 3 vari\u00e1veis:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14c23a38a656a0b7793fce158e93c71d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y,z) = 3x^5y^4 + 6x^3y^2z - 2y^6z^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"277\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Quanto ao grau absoluto do polin\u00f4mio, seu primeiro mon\u00f4mio \u00e9 de grau 9, o segundo termo do polin\u00f4mio \u00e9 de grau 6 e, por fim, o terceiro elemento do polin\u00f4mio \u00e9 de grau 8. Portanto, o grau absoluto do polin\u00f4mio de o problema \u00e9 9, pois \u00e9 o grau m\u00e1ximo de seus mon\u00f4mios.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-51f924b29a856b49d94b6e4161ee5168_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Grado absoluto de } P(x,y,z) = 9\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"253\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Por outro lado, o grau relativo refere-se a cada vari\u00e1vel individualmente e consiste no expoente m\u00e1ximo dessa vari\u00e1vel. Assim, o grau m\u00e1ximo da vari\u00e1vel <em>x<\/em> \u00e9 5, o grau relativo da vari\u00e1vel <em>y<\/em> \u00e9 6 e, finalmente, o grau em rela\u00e7\u00e3o \u00e0 letra <em>z<\/em> \u00e9 2.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e44a1c4820d800947fdfad9e2e4a018e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Grado relativo de } x = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"184\" style=\"vertical-align: -1px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1fdd90aecb2bae99ce30a9354f23812e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Grado relativo de } y = 6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"184\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b493f8f4a6e6090450c496652a5e166f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Grado relativo de } z = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"183\" style=\"vertical-align: -1px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Tipos-de-polinomios-segun-el-grado-de-sus-monomios\"><\/span> Tipos de polin\u00f4mios de acordo com o grau de seus mon\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Certos polin\u00f4mios particulares podem ser classificados de acordo com o grau de seus termos:<\/p>\n<ul>\n<li> <strong>Polin\u00f4mio ordenado<\/strong> : Um polin\u00f4mio \u00e9 ordenado se seus mon\u00f4mios forem escritos do grau mais alto para o grau mais baixo.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-815dd6636e1955ea61e9ac8b27a426be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = x^4 + 4x^3+6x^2 +3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> O polin\u00f4mio anterior \u00e9 ordenado porque seus mon\u00f4mios s\u00e3o ordenados por grau em ordem decrescente.<\/p>\n<ul>\n<li> <strong>Polin\u00f4mio completo<\/strong> : aquele polin\u00f4mio que possui todos os termos de todos os graus, desde o mon\u00f4mio de maior grau at\u00e9 o termo independente.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-278c4d4d2adf7e784c19c7760b0d9e3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = x^5 + 3x^4-5x^3+2x^2 +x+9\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"287\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Logicamente, o n\u00famero de termos em qualquer polin\u00f4mio completo \u00e9 igual ao grau do polin\u00f4mio mais 1.<\/p>\n<ul>\n<li> <strong>Polin\u00f4mio incompleto<\/strong> : Polin\u00f4mio em que falta um termo de certo grau entre o mon\u00f4mio de grau superior e o termo independente.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b6f18ecc498f892ea306c3bc154fb7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = x^5+4x^3-7x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Polin\u00f4mio homog\u00eaneo<\/strong> : Um polin\u00f4mio \u00e9 homog\u00eaneo quando todos os seus elementos t\u00eam o mesmo grau. Por exemplo, o seguinte polin\u00f4mio \u00e9 homog\u00eaneo porque todos os seus mon\u00f4mios s\u00e3o de grau 7.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-38210759b3d11648975eae20ac89fdde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y) =  6x^3y^4+2x^5y^2 -4x^6y\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"245\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Polin\u00f4mio heterog\u00eaneo<\/strong> : um polin\u00f4mio \u00e9 heterog\u00eaneo se pelo menos um de seus termos tiver grau diferente de qualquer um dos outros termos que comp\u00f5em o polin\u00f4mio.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0167d44da47b6687db1471857dc0a7a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y) =  4x^3+11x^5-6y^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"209\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> O polin\u00f4mio do exerc\u00edcio anterior possui dois mon\u00f4mios de mesmo grau (11x <sup>5<\/sup> e -6y <sup>5<\/sup> ), mas como 4x <sup>3<\/sup> tem grau diferente, \u00e9 um polin\u00f4mio heterog\u00eaneo.<\/p>\n<ul>\n<li> <strong>Polin\u00f4mios id\u00eanticos<\/strong> \u2013 Dois polin\u00f4mios s\u00e3o id\u00eanticos se os coeficientes dos termos do mesmo grau forem equivalentes.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-021f7dbd07b9ebc159a23f1644e524f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y) = x^6+3x^4-5x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"192\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-193b357b4614e16c10180d44ce0095e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x,y) = x^6+3x^4-5x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Polin\u00f4mio oposto<\/strong> : Dois polin\u00f4mios s\u00e3o opostos se seus mon\u00f4mios s\u00e3o exatamente iguais, mas de sinais opostos. <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d061069071e226e08110b2dfe676067a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = x^4+4x^2-3x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-81e91902303e7ba06c7e0881e29db6c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = -x^4-4x^2+3x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"212\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina explicamos o que \u00e9 o grau de um polin\u00f4mio (grau absoluto e grau relativo) e como saber qual \u00e9 o grau de um polin\u00f4mio. Voc\u00ea tamb\u00e9m poder\u00e1 ver v\u00e1rios exemplos de como o grau de um polin\u00f4mio \u00e9 determinado e, al\u00e9m disso, descobrir\u00e1 como os polin\u00f4mios s\u00e3o classificados de acordo com seu grau. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/\"> <span class=\"screen-reader-text\">Grau de um polin\u00f4mio<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[21],"tags":[],"class_list":["post-301","post","type-post","status-publish","format-standard","hentry","category-polinomios"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Grau de um polin\u00f4mio - Matoridade<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Grau de um polin\u00f4mio - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina explicamos o que \u00e9 o grau de um polin\u00f4mio (grau absoluto e grau relativo) e como saber qual \u00e9 o grau de um polin\u00f4mio. Voc\u00ea tamb\u00e9m poder\u00e1 ver v\u00e1rios exemplos de como o grau de um polin\u00f4mio \u00e9 determinado e, al\u00e9m disso, descobrir\u00e1 como os polin\u00f4mios s\u00e3o classificados de acordo com seu grau. &hellip; Grau de um polin\u00f4mio Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T15:21:06+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7fcca51a02c5abdfd8a12ef79c2785f_l3.png\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Grau de um polin\u00f4mio\",\"datePublished\":\"2023-07-06T15:21:06+00:00\",\"dateModified\":\"2023-07-06T15:21:06+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/\"},\"wordCount\":815,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Polin\u00f4mios\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/\",\"url\":\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/\",\"name\":\"Grau de um polin\u00f4mio - Matoridade\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/#website\"},\"datePublished\":\"2023-07-06T15:21:06+00:00\",\"dateModified\":\"2023-07-06T15:21:06+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Grau de um polin\u00f4mio\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/pt\/#website\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"name\":\"Mathority\",\"description\":\"Onde a curiosidade encontra o c\u00e1lculo!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/pt\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\",\"name\":\"Equipe Mathoridade\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Equipe Mathoridade\"},\"sameAs\":[\"http:\/\/mathority.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Grau de um polin\u00f4mio - Matoridade","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/","og_locale":"pt_BR","og_type":"article","og_title":"Grau de um polin\u00f4mio - Matoridade","og_description":"Nesta p\u00e1gina explicamos o que \u00e9 o grau de um polin\u00f4mio (grau absoluto e grau relativo) e como saber qual \u00e9 o grau de um polin\u00f4mio. Voc\u00ea tamb\u00e9m poder\u00e1 ver v\u00e1rios exemplos de como o grau de um polin\u00f4mio \u00e9 determinado e, al\u00e9m disso, descobrir\u00e1 como os polin\u00f4mios s\u00e3o classificados de acordo com seu grau. &hellip; Grau de um polin\u00f4mio Leia mais &raquo;","og_url":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/","article_published_time":"2023-07-06T15:21:06+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7fcca51a02c5abdfd8a12ef79c2785f_l3.png"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"4 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Grau de um polin\u00f4mio","datePublished":"2023-07-06T15:21:06+00:00","dateModified":"2023-07-06T15:21:06+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/"},"wordCount":815,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"articleSection":["Polin\u00f4mios"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/","url":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/","name":"Grau de um polin\u00f4mio - Matoridade","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/#website"},"datePublished":"2023-07-06T15:21:06+00:00","dateModified":"2023-07-06T15:21:06+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/pt\/grau-de-um-polinomio\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/pt\/"},{"@type":"ListItem","position":2,"name":"Grau de um polin\u00f4mio"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/pt\/#website","url":"https:\/\/mathority.org\/pt\/","name":"Mathority","description":"Onde a curiosidade encontra o c\u00e1lculo!","publisher":{"@id":"https:\/\/mathority.org\/pt\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/pt\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"pt-BR"},{"@type":"Organization","@id":"https:\/\/mathority.org\/pt\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/pt\/","logo":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00","name":"Equipe Mathoridade","image":{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Equipe Mathoridade"},"sameAs":["http:\/\/mathority.org\/pt"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/301","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/comments?post=301"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/posts\/301\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/media?parent=301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/categories?post=301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/pt\/wp-json\/wp\/v2\/tags?post=301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}