{"id":321,"date":"2023-07-06T08:39:49","date_gmt":"2023-07-06T08:39:49","guid":{"rendered":"https:\/\/mathority.org\/pt\/polinomios-iguais\/"},"modified":"2023-07-06T08:39:49","modified_gmt":"2023-07-06T08:39:49","slug":"polinomios-iguais","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/polinomios-iguais\/","title":{"rendered":"Polin\u00f4mios iguais"},"content":{"rendered":"<p>Aqui voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o de quando dois polin\u00f4mios s\u00e3o iguais. Voc\u00ea tamb\u00e9m poder\u00e1 ver v\u00e1rios exemplos de polin\u00f4mios iguais e, al\u00e9m disso, as propriedades deste tipo de polin\u00f4mios. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFCuando-dos-polinomios-son-iguales\"><\/span> Quando dois polin\u00f4mios s\u00e3o iguais?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A defini\u00e7\u00e3o de polin\u00f4mios iguais \u00e9 a seguinte:<\/p>\n<p> <strong>Dois polin\u00f4mios s\u00e3o iguais se tiverem o mesmo grau e, al\u00e9m disso, os coeficientes dos termos do mesmo grau forem id\u00eanticos.<\/strong><\/p>\n<p> Por exemplo, os dois polin\u00f4mios a seguir s\u00e3o iguais:<\/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-8a0299034a83843a3663cf19ec234bf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = x^4+3x^2-7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"158\" 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-ba81ebb0cdd47d643d5b20484699c076_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = 3x^2+x^4-7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"158\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Os 2 polin\u00f4mios anteriores s\u00e3o iguais porque ambos s\u00e3o de grau 4 e os valores dos coeficientes de seus termos coincidem: os coeficientes dos termos do quarto grau s\u00e3o 1, os coeficientes dos mon\u00f4mios do segundo grau s\u00e3o 3, e os coeficientes dos Elementos de grau zero (termo independente) s\u00e3o -7.<\/p>\n<p> Uma das aplica\u00e7\u00f5es dos polin\u00f4mios iguais \u00e9 que eles s\u00e3o muito \u00fateis para <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/fracoes-algebricas-operacoes-simplificadas-adicao-subtracao-multiplicacao-divisao-exercicios-resolvidos\/\">simplificar fra\u00e7\u00f5es alg\u00e9bricas<\/a><\/span><\/strong> . Embora simplificar uma fra\u00e7\u00e3o alg\u00e9brica seja um procedimento complicado, fica muito mais f\u00e1cil quando os polin\u00f4mios que comp\u00f5em a fra\u00e7\u00e3o s\u00e3o iguais. Voc\u00ea pode ver como as fra\u00e7\u00f5es alg\u00e9bricas s\u00e3o simplificadas clicando no link. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-polinomios-iguales\"><\/span> Exemplos de polin\u00f4mios iguais<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de sabermos o que significa dois polin\u00f4mios serem iguais, veremos v\u00e1rios exemplos desse tipo de polin\u00f4mio para finalizar a compreens\u00e3o do conceito:<\/p>\n<ul>\n<li> Polin\u00f4mios iguais de grau 3:<\/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-03c5dba295b352c1d711f5b7be05bd00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 2x^3-5x^2+9x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"208\" 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-72963c14d81b24e4962d2baff09e8dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = 2x^3+9x+3-5x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Polin\u00f4mios iguais 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-426c96c3c2fe57e8c8730dd9a9d4a3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = -x^4+7x^3-2x-10\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"222\" 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-aee695401a09e4b83971237d2aaf6f63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = -10-x^4+7x^3-2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"222\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Polin\u00f4mios iguais de grau 6: <\/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-082b4003e32b0f409edc0f10464f3853_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 5x^6+4x^5-3x^2-x+8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-5ca6018077e6302d65ec3ad73047c63a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = 5x^6+8-x+4x^5-3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Polinomios-iguales-y-semejantes\"><\/span> Polin\u00f4mios iguais e semelhantes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Voc\u00ea certamente j\u00e1 domina o significado de polin\u00f4mios iguais. No entanto, deve-se notar que polin\u00f4mios iguais n\u00e3o devem ser confundidos com polin\u00f4mios semelhantes.<\/p>\n<p> A <strong>diferen\u00e7a entre polin\u00f4mios iguais e polin\u00f4mios semelhantes<\/strong> \u00e9 que os termos de polin\u00f4mios iguais devem ser exatamente iguais (como o nome sugere), por outro lado, polin\u00f4mios semelhantes s\u00e3o aqueles polin\u00f4mios cujos termos t\u00eam a mesma parte literal, mas n\u00e3o necessariamente t\u00eam o mesmos coeficientes.<\/p>\n<p> Por exemplo, os dois polin\u00f4mios a seguir s\u00e3o semelhantes porque todos os mon\u00f4mios de grau equivalente t\u00eam a mesma parte literal, mas seus coeficientes n\u00e3o s\u00e3o iguais:<\/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-e6a38c78f1ee443340e77b2985e2f178_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 2x^5-3x^3+4x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" 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-2c74511ea7e56b6bc21e6d0906e0006d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = x^5+2x^3+7x-6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Portanto, todos os polin\u00f4mios iguais tamb\u00e9m s\u00e3o polin\u00f4mios semelhantes, pois todos os seus respectivos termos de mesmo grau possuem a mesma parte literal. Por outro lado, polin\u00f4mios semelhantes n\u00e3o precisam ser iguais. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-de-los-polinomios-iguales\"><\/span> Propriedades de polin\u00f4mios iguais<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Todos os polin\u00f4mios iguais atendem \u00e0s seguintes caracter\u00edsticas em rela\u00e7\u00e3o \u00e0s opera\u00e7\u00f5es entre si:<\/p>\n<ul>\n<li> Subtrair dois polin\u00f4mios iguais resulta no polin\u00f4mio nulo (ou 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-9df72f4b4014dbd556109a24a083c827_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) - P(x) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Caso voc\u00ea tenha alguma d\u00favida de como fazer, no link a seguir voc\u00ea poder\u00e1 ver como calcular uma <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/subtracao-de-polinomios-exemplos-exercicios-resolvidos-subtracao\/\">subtra\u00e7\u00e3o de polin\u00f4mios<\/a><\/span><\/strong> . L\u00e1 voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o dos dois m\u00e9todos existentes para subtrair polin\u00f4mios (vertical e horizontal) e poder\u00e1 praticar com exerc\u00edcios resolvidos passo a passo.<\/p>\n<ul>\n<li> A soma de dois polin\u00f4mios iguais equivale a multiplicar um desses polin\u00f4mios por 2.<\/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-2ad67b140c30f1d2975bb3078df7f247_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) +P(x) = 2P(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"167\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Caso voc\u00ea n\u00e3o tenha entendido completamente como essas duas opera\u00e7\u00f5es s\u00e3o realizadas, deixo para voc\u00eas estas p\u00e1ginas onde \u00e9 explicado como <a href=\"https:\/\/mathority.org\/pt\/soma-de-polinomios-exemplos-adicao-de-exercicios-resolvidos\/\"><strong><span style=\"text-decoration: underline;\">adicionar polin\u00f4mios<\/span><\/strong><\/a> e como <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/multiplicacao-de-polinomios-exemplos-exercicios-produto-resolvido-multiplicacao\/\">multiplicar polin\u00f4mios<\/a><\/span><\/strong> . Em cada uma dessas duas p\u00e1ginas voc\u00ea poder\u00e1 ver exemplos, praticar com exerc\u00edcios resolvidos e descobrir quais s\u00e3o as propriedades de cada opera\u00e7\u00e3o.<\/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 de quando dois polin\u00f4mios s\u00e3o iguais. Voc\u00ea tamb\u00e9m poder\u00e1 ver v\u00e1rios exemplos de polin\u00f4mios iguais e, al\u00e9m disso, as propriedades deste tipo de polin\u00f4mios. Quando dois polin\u00f4mios s\u00e3o iguais? A defini\u00e7\u00e3o de polin\u00f4mios iguais \u00e9 a seguinte: Dois polin\u00f4mios s\u00e3o iguais se tiverem o mesmo grau e, al\u00e9m disso, os &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/polinomios-iguais\/\"> <span class=\"screen-reader-text\">Polin\u00f4mios iguais<\/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-321","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\u00f4mios iguais - 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\/polinomios-iguais\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Polin\u00f4mios iguais - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o de quando dois polin\u00f4mios s\u00e3o iguais. 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Voc\u00ea tamb\u00e9m poder\u00e1 ver v\u00e1rios exemplos de polin\u00f4mios iguais e, al\u00e9m disso, as propriedades deste tipo de polin\u00f4mios. Quando dois polin\u00f4mios s\u00e3o iguais? 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