{"id":312,"date":"2023-07-06T11:45:56","date_gmt":"2023-07-06T11:45:56","guid":{"rendered":"https:\/\/mathority.org\/pt\/termo-independente-de-um-polinomio\/"},"modified":"2023-07-06T11:45:56","modified_gmt":"2023-07-06T11:45:56","slug":"termo-independente-de-um-polinomio","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/termo-independente-de-um-polinomio\/","title":{"rendered":"Termo independente de um polin\u00f4mio"},"content":{"rendered":"<p>Nesta p\u00e1gina explicamos o que \u00e9 o termo independente de um polin\u00f4mio e como ele \u00e9 calculado. Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exemplos de como identificar o termo independente de diferentes polin\u00f4mios e, ainda, praticar com exerc\u00edcios resolvidos. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFCual-es-el-termino-independiente-de-un-polinomio\"><\/span> Qual \u00e9 o termo independente de um polin\u00f4mio?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A defini\u00e7\u00e3o do termo independente de um polin\u00f4mio \u00e9 a seguinte:<\/p>\n<p> <strong>Em matem\u00e1tica, o termo independente de um polin\u00f4mio \u00e9 o termo que n\u00e3o possui vari\u00e1vel. Portanto, o termo independente de um polin\u00f4mio corresponde ao mon\u00f4mio de grau zero do polin\u00f4mio.<\/strong><\/p>\n<p> Por exemplo, o termo independente do seguinte polin\u00f4mio \u00e9 7:<\/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-ce8613fa93699f08e1eb6390b3c1510e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=4x^3-5x^2+3x+7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> No polin\u00f4mio do exemplo anterior, o termo que n\u00e3o possui parte literal, ou seja, n\u00e3o possui x, \u00e9 o n\u00famero 7. Por isso, o termo independente do referido polin\u00f4mio \u00e9 7.<\/p>\n<p> Embora o termo independente de um polin\u00f4mio pare\u00e7a um conceito muito simples, saiba que ele \u00e9 muito \u00fatil para alguns c\u00e1lculos polinomiais. Por exemplo, o procedimento para encontrar as <a href=\"https:\/\/mathority.org\/pt\/raizes-de-um-polinomio\/\"><strong><span style=\"text-decoration: underline;\">ra\u00edzes de um polin\u00f4mio<\/span><\/strong><\/a> come\u00e7a no seu termo independente. Se quiser saber mais sobre como encontrar as ra\u00edzes (ou zeros) de um polin\u00f4mio, voc\u00ea pode conferir este link, onde tamb\u00e9m pode ver exemplos e praticar com exerc\u00edcios resolvidos passo a passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-terminos-independientes-de-polinomios\"><\/span> Exemplos de termos independentes de polin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de sabermos o significado do termo independente de um polin\u00f4mio, veremos v\u00e1rios exemplos de como encontrar o termo independente de um polin\u00f4mio:<\/p>\n<ul>\n<li> Exemplo de termo independente de um polin\u00f4mio de grau 4:<\/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-ea2df957af119e4f78ed6e73fae9f916_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^4+6x^3+2x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> O polin\u00f4mio neste exemplo \u00e9 um polin\u00f4mio m\u00f4nico e o termo que n\u00e3o possui vari\u00e1vel \u00e9 5, portanto o valor do termo independente do polin\u00f4mio \u00e9 5.<\/p>\n<ul>\n<li> Exemplo de termo independente de um polin\u00f4mio de grau 5:<\/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-e7a73708ecf28758b495ca20f81fc737_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=3x^5-4x^3+9x^2-2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"214\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> O elemento deste polin\u00f4mio que n\u00e3o vem acompanhado da vari\u00e1vel x \u00e9 -2, \u00e9 portanto o termo independente do polin\u00f4mio. Observe que o sinal negativo do n\u00famero tamb\u00e9m est\u00e1 inclu\u00eddo no termo independente.<\/p>\n<ul>\n<li> Exemplo de termo independente de um polin\u00f4mio de grau 8:<\/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-363427dbde637972f4ceb34be271c5fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=-3x^8+4x^5+3x^2+7x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"269\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Todos os mon\u00f4mios neste polin\u00f4mio t\u00eam uma vari\u00e1vel exceto +1, ent\u00e3o o termo independente do polin\u00f4mio \u00e9 +1.<\/p>\n<p> Finalmente, uma das propriedades do termo independente \u00e9 que o <a href=\"https:\/\/mathority.org\/pt\/valor-numerico-de-um-polinomio-exemplos-exercicios-resolvidos\/\"><strong><span style=\"text-decoration: underline;\">valor num\u00e9rico de um polin\u00f4mio<\/span><\/strong><\/a> para x=0 \u00e9 sempre igual ao seu termo independente. Se voc\u00ea est\u00e1 mais interessado nessa curiosidade, pode consultar na p\u00e1gina do link como \u00e9 calculado o valor num\u00e9rico de um polin\u00f4mio, al\u00e9m disso voc\u00ea tamb\u00e9m encontrar\u00e1 v\u00e1rios exemplos de como isso \u00e9 feito e poder\u00e1 praticar com exerc\u00edcios resolvidos passo a passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicio-resuelto-sobre-el-termino-independiente-de-un-polinomio\"><\/span> Exerc\u00edcio resolvido sobre o termo independente de um polin\u00f4mio<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para finalizar a assimila\u00e7\u00e3o do que \u00e9 o termo independente de um polin\u00f4mio, sugerimos que voc\u00ea fa\u00e7a o exerc\u00edcio que resolvemos a seguir:<\/p>\n<ul>\n<li> Dado o polin\u00f4mio\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4434cf5fac5ca67f90cd6bcba9ed6509_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=3x^2-5x+k,\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"164\" style=\"vertical-align: -5px;\"><\/p>\n<p> calcula o valor do termo independente<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> para que fique cheio<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-142bc42641d95cafd40829ecf9cc6d7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=6.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p> A primeira coisa a fazer para resolver esse problema \u00e9 tentar determinar<\/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-499303bbaf114c436c69f7518630f4e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2),\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -5px;\"><\/p>\n<p> Ainda:<\/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-23a52b6ccc36123219561fe3598346b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=3\\cdot 2^2-5\\cdot 2+k\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"181\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Calculamos a pot\u00eancia:<\/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-c9e1fcf46640fd9eb45f22e317dcfb62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=3\\cdot 4-5\\cdot 2+k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"174\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Fazemos as multiplica\u00e7\u00f5es:<\/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-4c623605b0646c2e6e30e4d6672b60d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=12-10+k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"148\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> E subtra\u00edmos como termos:<\/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-599a2f8ab67b5980634c7a9be2453480_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=2+k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"100\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Assim, para que a condi\u00e7\u00e3o do enunciado seja atendida, \u00e9 necess\u00e1rio equalizar a express\u00e3o alg\u00e9brica obtida a 6:<\/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-02c8fb62c4da8667e77d605fe702580c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" 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-e645fd7cf3517abb262230848bc72e1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2+k=6\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Portanto, \u00e9 suficiente resolver a equa\u00e7\u00e3o resultante:<\/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-1a2efb27129bffdf3913c4e130e19786_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=6-2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"72\" style=\"vertical-align: 0px;\"><\/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-1c156d574bb12e97890c19219cdbbed4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{k=4}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Concluindo, o termo independente do polin\u00f4mio deve ser 4.<\/p>\n<p> Finalmente, voc\u00ea deve saber que o termo independente de um polin\u00f4mio tamb\u00e9m \u00e9 importante para aplicar corretamente a regra de Ruffini. Caso voc\u00ea n\u00e3o saiba o que \u00e9, a regra de Ruffini \u00e9 um m\u00e9todo usado para dividir polin\u00f4mios rapidamente. Aqui voc\u00ea pode ver <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/regras-resolvidas-exemplos-exercicios-ruffini\/\">como fazer a regra de Ruffini<\/a><\/span><\/strong> e como ela se relaciona com o termo independente de um polin\u00f4mio.<\/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 termo independente de um polin\u00f4mio e como ele \u00e9 calculado. Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exemplos de como identificar o termo independente de diferentes polin\u00f4mios e, ainda, praticar com exerc\u00edcios resolvidos. Qual \u00e9 o termo independente de um polin\u00f4mio? A defini\u00e7\u00e3o do termo independente de um polin\u00f4mio &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/termo-independente-de-um-polinomio\/\"> <span class=\"screen-reader-text\">Termo independente 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-312","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>Termo independente 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\/termo-independente-de-um-polinomio\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Termo independente de um polin\u00f4mio - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina explicamos o que \u00e9 o termo independente de um polin\u00f4mio e como ele \u00e9 calculado. 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Al\u00e9m disso, voc\u00ea poder\u00e1 ver diversos exemplos de como identificar o termo independente de diferentes polin\u00f4mios e, ainda, praticar com exerc\u00edcios resolvidos. Qual \u00e9 o termo independente de um polin\u00f4mio? A defini\u00e7\u00e3o do termo independente de um polin\u00f4mio &hellip; Termo independente de um polin\u00f4mio Leia mais &raquo;","og_url":"https:\/\/mathority.org\/pt\/termo-independente-de-um-polinomio\/","article_published_time":"2023-07-06T11:45:56+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce8613fa93699f08e1eb6390b3c1510e_l3.png"}],"author":"Equipe Mathoridade","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Equipe Mathoridade","Est. tempo de leitura":"3 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/pt\/termo-independente-de-um-polinomio\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/pt\/termo-independente-de-um-polinomio\/"},"author":{"name":"Equipe Mathoridade","@id":"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00"},"headline":"Termo independente de um polin\u00f4mio","datePublished":"2023-07-06T11:45:56+00:00","dateModified":"2023-07-06T11:45:56+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/pt\/termo-independente-de-um-polinomio\/"},"wordCount":623,"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\/termo-independente-de-um-polinomio\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/pt\/termo-independente-de-um-polinomio\/","url":"https:\/\/mathority.org\/pt\/termo-independente-de-um-polinomio\/","name":"Termo independente de um polin\u00f4mio - 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