{"id":292,"date":"2023-07-06T17:50:07","date_gmt":"2023-07-06T17:50:07","guid":{"rendered":"https:\/\/mathority.org\/pt\/polinomio-heterogeneo\/"},"modified":"2023-07-06T17:50:07","modified_gmt":"2023-07-06T17:50:07","slug":"polinomio-heterogeneo","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/polinomio-heterogeneo\/","title":{"rendered":"Polin\u00f4mio heterog\u00eaneo"},"content":{"rendered":"<p>Aqui voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o do que s\u00e3o polin\u00f4mios heterog\u00eaneos e, al\u00e9m disso, poder\u00e1 ver exemplos deste tipo de polin\u00f4mios. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-polinomio-heterogeneo\"><\/span> O que \u00e9 um polin\u00f4mio heterog\u00eaneo?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A defini\u00e7\u00e3o matem\u00e1tica do polin\u00f4mio heterog\u00eaneo \u00e9 a seguinte:<\/p>\n<p> <strong>Em matem\u00e1tica, um polin\u00f4mio heterog\u00eaneo \u00e9 um polin\u00f4mio em que todos os termos n\u00e3o t\u00eam o mesmo grau.<\/strong><\/p>\n<p> Portanto, se pelo menos um mon\u00f4mio de um determinado polin\u00f4mio tem grau diferente de outro mon\u00f4mio que faz parte do mesmo polin\u00f4mio, isso significa que diz que o polin\u00f4mio \u00e9 heterog\u00eaneo.<\/p>\n<p> Por exemplo, o seguinte polin\u00f4mio \u00e9 heterog\u00eaneo:<\/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-f64e4da14cab0807846e2880e36d5569_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)= x^3+5x^2-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"158\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Na verdade, \u00e9 um polin\u00f4mio heterog\u00eaneo porque possui termos de graus diferentes: x <sup>3<\/sup> \u00e9 de grau 3, 5x <sup>2<\/sup> \u00e9 de grau 2 e -4 \u00e9 de grau 0, pois \u00e9 um termo independente e n\u00e3o possui vari\u00e1vel.<\/p>\n<p> Por outro lado, como voc\u00ea deve saber, este polin\u00f4mio tamb\u00e9m \u00e9 um <a href=\"https:\/\/mathority.org\/pt\/polinomio-incompleto\/\"><strong><span style=\"text-decoration: underline;\">polin\u00f4mio incompleto<\/span><\/strong><\/a> . Se voc\u00ea ainda n\u00e3o est\u00e1 familiarizado com este conceito, recomendamos dar uma olhada neste link onde explicamos o que significa um polin\u00f4mio ser incompleto. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-polinomios-heterogeneos\"><\/span> Exemplos de polin\u00f4mios heterog\u00eaneos<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos o significado alg\u00e9brico de um polin\u00f4mio heterog\u00eaneo, vejamos agora alguns exemplos de polin\u00f4mios heterog\u00eaneos para finalizar a compreens\u00e3o do conceito:<\/p>\n<ul>\n<li> Exemplo de um polin\u00f4mio heterog\u00eaneo com uma vari\u00e1vel<\/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-b31cf393c3f304bdd3608d01c4a05953_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)= 3x^4+2x^3+8x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"177\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Exemplo de um polin\u00f4mio heterog\u00eaneo com duas vari\u00e1veis:<\/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-87b36aaa563ed2b970108a9076e80586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y)= x^5+3y^5+4x^2y\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"201\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Como voc\u00ea pode ver no exemplo anterior, um polin\u00f4mio heterog\u00eaneo tamb\u00e9m pode ter termos de graus semelhantes. Neste caso x <sup>5<\/sup> e 3y <sup>5<\/sup> s\u00e3o ambos de quinto grau, por\u00e9m, o mon\u00f4mio 4x <sup>2<\/sup> y \u00e9 de terceiro grau e, portanto, o polin\u00f4mio \u00e9 heterog\u00eaneo pois nem todos os seus termos possuem o mesmo grau.<\/p>\n<ul>\n<li> Exemplo de um polin\u00f4mio heterog\u00eaneo de 3 vari\u00e1veis:<\/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-3667f64b92946ae230531c3d9605395d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(a,b,c)=5a^3b^2y + 5a^5b^3y -7a^2by^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"286\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Por fim, voc\u00ea deve saber que existe um tipo de polin\u00f4mio que, pelas suas caracter\u00edsticas, \u00e9 muito diferente dos polin\u00f4mios heterog\u00eaneos, que s\u00e3o polin\u00f4mios homog\u00eaneos. Mas \u00e9 precisamente por esta raz\u00e3o que voc\u00ea precisa saber como os polin\u00f4mios heterog\u00eaneos diferem dos polin\u00f4mios homog\u00eaneos. Voc\u00ea o encontrar\u00e1 na explica\u00e7\u00e3o do que s\u00e3o <a href=\"https:\/\/mathority.org\/pt\/exemplos-de-polinomios-homogeneos\/\"><strong><span style=\"text-decoration: underline;\">polin\u00f4mios homog\u00eaneos<\/span><\/strong><\/a> , onde, al\u00e9m disso, poder\u00e1 ver exemplos de polin\u00f4mios homog\u00eaneos e quais s\u00e3o todas as suas propriedades.<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Aqui voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o do que s\u00e3o polin\u00f4mios heterog\u00eaneos e, al\u00e9m disso, poder\u00e1 ver exemplos deste tipo de polin\u00f4mios. O que \u00e9 um polin\u00f4mio heterog\u00eaneo? A defini\u00e7\u00e3o matem\u00e1tica do polin\u00f4mio heterog\u00eaneo \u00e9 a seguinte: Em matem\u00e1tica, um polin\u00f4mio heterog\u00eaneo \u00e9 um polin\u00f4mio em que todos os termos n\u00e3o t\u00eam o mesmo grau. Portanto, se &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/polinomio-heterogeneo\/\"> <span class=\"screen-reader-text\">Polin\u00f4mio heterog\u00eaneo<\/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":[38],"tags":[],"class_list":["post-292","post","type-post","status-publish","format-standard","hentry","category-tipos-de-polinomios"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Polin\u00f4mio heterog\u00eaneo - 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\/polinomio-heterogeneo\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Polin\u00f4mio heterog\u00eaneo - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o do que s\u00e3o polin\u00f4mios heterog\u00eaneos e, al\u00e9m disso, poder\u00e1 ver exemplos deste tipo de polin\u00f4mios. O que \u00e9 um polin\u00f4mio heterog\u00eaneo? A defini\u00e7\u00e3o matem\u00e1tica do polin\u00f4mio heterog\u00eaneo \u00e9 a seguinte: Em matem\u00e1tica, um polin\u00f4mio heterog\u00eaneo \u00e9 um polin\u00f4mio em que todos os termos n\u00e3o t\u00eam o mesmo grau. 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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\/polinomio-heterogeneo\/","og_locale":"pt_BR","og_type":"article","og_title":"Polin\u00f4mio heterog\u00eaneo - Matoridade","og_description":"Aqui voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o do que s\u00e3o polin\u00f4mios heterog\u00eaneos e, al\u00e9m disso, poder\u00e1 ver exemplos deste tipo de polin\u00f4mios. O que \u00e9 um polin\u00f4mio heterog\u00eaneo? A defini\u00e7\u00e3o matem\u00e1tica do polin\u00f4mio heterog\u00eaneo \u00e9 a seguinte: Em matem\u00e1tica, um polin\u00f4mio heterog\u00eaneo \u00e9 um polin\u00f4mio em que todos os termos n\u00e3o t\u00eam o mesmo grau. 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