{"id":54,"date":"2023-09-17T07:26:59","date_gmt":"2023-09-17T07:26:59","guid":{"rendered":"https:\/\/mathority.org\/pt\/divisao-de-polinomios-exemplos-exercicios-resolvidos-dividir\/"},"modified":"2023-09-17T07:26:59","modified_gmt":"2023-09-17T07:26:59","slug":"divisao-de-polinomios-exemplos-exercicios-resolvidos-dividir","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/divisao-de-polinomios-exemplos-exercicios-resolvidos-dividir\/","title":{"rendered":"Divis\u00e3o polinomial"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea descobrir\u00e1 como dividir polin\u00f4mios, tanto a divis\u00e3o de um polin\u00f4mio por um mon\u00f4mio quanto a divis\u00e3o de um polin\u00f4mio por outro polin\u00f4mio. Voc\u00ea tamb\u00e9m poder\u00e1 ver exemplos de divis\u00e3o de polin\u00f4mios e praticar exerc\u00edcios resolvidos passo a passo. Al\u00e9m disso, voc\u00ea encontrar\u00e1 as propriedades desta opera\u00e7\u00e3o polinomial.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Division-polinomica-o-polinomial\"><\/span> Divis\u00e3o polinomial (ou polinomial)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Antes de vermos exatamente como dois polin\u00f4mios s\u00e3o divididos, revisaremos brevemente os conceitos de divis\u00e3o polinomial, para que ent\u00e3o seja mais f\u00e1cil entender o m\u00e9todo que vamos utilizar.<\/p>\n<p> Quatro polin\u00f4mios est\u00e3o envolvidos em uma divis\u00e3o polinomial:<\/p>\n<ul>\n<li> <strong>Dividendo<\/strong> : o polin\u00f4mio dividido.<\/li>\n<li> <strong>Divisor<\/strong> : o polin\u00f4mio que divide o dividendo.<\/li>\n<li> <strong>Quociente<\/strong> : resultado da divis\u00e3o do dividendo pelo divisor.<\/li>\n<li> <strong>Resto<\/strong> (ou res\u00edduo): o polin\u00f4mio restante na divis\u00e3o entre os dois polin\u00f4mios. <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/division-de-polynomes-en-ligne.jpg\" alt=\"divis\u00e3o de polin\u00f4mios on-line\" class=\"wp-image-727\" width=\"384\" height=\"171\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Por outro lado, voc\u00ea tamb\u00e9m deve saber que existem dois tipos de divis\u00e3o entre polin\u00f4mios:<\/p>\n<ul>\n<li> <strong>Divis\u00e3o exata de polin\u00f4mios<\/strong> : uma divis\u00e3o entre polin\u00f4mios \u00e9 exata quando o resto \u00e9 zero. Neste caso, o dividendo polinomial \u00e9 igual ao divisor multiplicado pelo quociente.<\/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-03b0f25c6ee662a18b5b13eb01dfca53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(x)=d(x) \\cdot c(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Al\u00e9m disso, neste caso, o dividendo<\/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-0170b983fcc648c0a50265cc7143c9ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u00e9 um m\u00faltiplo do divisor<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ab3160465c716f536f72ff05019a7fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"><\/p>\n<p> e o quociente<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a600690e2f19c13f9420f114ce2783ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c(x).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"36\" style=\"vertical-align: -5px;\"><\/p>\n<p> Da mesma forma, o divisor polinomial e o quociente polinomial s\u00e3o ambos divisores do dividendo.<\/p>\n<ul>\n<li> <strong>Divis\u00e3o inteira de polin\u00f4mios<\/strong> : em uma divis\u00e3o inteira (ou inexata) de polin\u00f4mios o resto \u00e9 diferente de zero (0). Ent\u00e3o, a propriedade fundamental da divis\u00e3o polinomial \u00e9 satisfeita:<\/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-2657eeecea1011960aa78859c32b354f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(x)=d(x) \\cdot c(x) + R(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Agora que vimos o que \u00e9 dividir polin\u00f4mios, vamos ver como dividir polin\u00f4mios entre si. Mais precisamente, explicaremos primeiro a divis\u00e3o entre um polin\u00f4mio e um mon\u00f4mio e depois a divis\u00e3o entre 2 polin\u00f4mios. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Division-de-un-polinomio-entre-un-monomio\"><\/span> Divis\u00e3o de um polin\u00f4mio por um mon\u00f4mio<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Antes de ver como dividir um polin\u00f4mio por um mon\u00f4mio, vamos primeiro lembrar como os mon\u00f4mios s\u00e3o divididos entre eles, pois \u00e9 necess\u00e1rio conhec\u00ea-lo para poder fazer este tipo de opera\u00e7\u00e3o polinomial.<\/p>\n<p> A divis\u00e3o de dois mon\u00f4mios envolve dividir seus coeficientes entre si e suas partes literais entre si, ou seja, dividem-se os coeficientes dos mon\u00f4mios e subtraem-se os expoentes das vari\u00e1veis que possuem a mesma base. Veja o exemplo a seguir:<\/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-2cd82fa96e7489279cd2a3dda6f307e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^5: 3x^2 =  \\cfrac{12x^5}{3x^2}=(12:3) x^{5-2} = 4x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"301\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Agora vamos ver o que envolve a divis\u00e3o de um polin\u00f4mio por um mon\u00f4mio:<\/p>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Em matem\u00e1tica, para resolver a <strong>divis\u00e3o de um polin\u00f4mio por um mon\u00f4mio,<\/strong> cada termo do polin\u00f4mio \u00e9 dividido pelo mon\u00f4mio. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/division-dun-polynome-par-un-monome.jpg\" alt=\"divis\u00e3o de um polin\u00f4mio por um mon\u00f4mio\" class=\"wp-image-734\" width=\"332\" height=\"267\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Observe no exemplo de divis\u00e3o anterior que ao dividir mon\u00f4mios ou polin\u00f4mios voc\u00ea tamb\u00e9m deve levar em considera\u00e7\u00e3o a regra dos sinais. Na verdade, um erro muito comum nas divis\u00f5es entre polin\u00f4mios e mon\u00f4mios \u00e9 errar o sinal de um termo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Division-de-un-polinomio-entre-otro-polinomio\"><\/span> Divis\u00e3o de um polin\u00f4mio por outro polin\u00f4mio<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para dividir dois polin\u00f4mios, \u00e9 necess\u00e1rio seguir um procedimento, ent\u00e3o vamos ver como fica o m\u00e9todo de divis\u00e3o de polin\u00f4mios, tamb\u00e9m chamado de divis\u00e3o longa de polin\u00f4mios, resolvendo um exemplo passo a passo:<\/p>\n<ul>\n<li> Calcule o resultado da divis\u00e3o do polin\u00f4mio\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a80be6e42ac3b3c6528958bbfa21f92c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"><\/p>\n<p> entre o polin\u00f4mio<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-12d5846d8a96763047fb4c9f458420f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" style=\"vertical-align: -5px;\"><\/p>\n<p> Sendo os dois polin\u00f4mios:<\/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-ca77e74e7adc7c5d4ad240dde49f1cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) =x^3+4x^2+12 \\qquad \\qquad Q(x) =x-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"340\" 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-08a81d992ddcff769763ef2424236efe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{P(x)}{Q(x)} = \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"70\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> A primeira coisa a fazer \u00e9 colocar os polin\u00f4mios na forma de divis\u00e3o. \u00c0 esquerda escrevemos o numerador da fra\u00e7\u00e3o (polin\u00f4mio dividendo) e \u00e0 direita colocamos o denominador da fra\u00e7\u00e3o (polin\u00f4mio divisor): <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/comment-diviser-les-polynomes.jpg\" alt=\"como dividir polin\u00f4mios\" class=\"wp-image-740\" width=\"387\" height=\"39\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-background\" style=\"background-color:#fffde7\"> <strong>Aten\u00e7\u00e3o:<\/strong> Se um polin\u00f4mio n\u00e3o possui um mon\u00f4mio de certo grau, devemos deixar um espa\u00e7o em seu lugar. Por exemplo, o polin\u00f4mio<\/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-742664589ea1a5ebbade880442ef5a31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+4x^2+12\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\"><\/p>\n<p> N\u00e3o h\u00e1 per\u00edodo de primeiro ano, portanto h\u00e1 um espa\u00e7o em branco. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/division-de-polynomes-quand-un-terme-manque.jpg\" alt=\"divis\u00e3o de polin\u00f4mios quando falta um termo\" class=\"wp-image-743\" width=\"387\" height=\"75\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Assim que tivermos os polin\u00f4mios no lugar, vamos encontrar o quociente. E para encontrar o primeiro termo do quociente devemos dividir o primeiro termo do dividendo pelo primeiro termo do divisor: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/regles-de-division-de-polynomes.jpg\" alt=\"regras para dividir polin\u00f4mios\" class=\"wp-image-744\" width=\"84\" height=\"58\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> E colocamos o resultado da divis\u00e3o no lugar do quociente: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/division-de-polynomes-quotient-avec-x.jpg\" alt=\"como dividir dois polin\u00f4mios\" class=\"wp-image-763\" width=\"387\" height=\"74\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Agora multiplicamos o termo encontrado por cada elemento do divisor, e colocamos cada resultado abaixo do dividendo em sua coluna correspondente <strong>, mudando seu sinal<\/strong> : <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-32\">\n<div class=\"wp-block-column is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/division-de-polynomes-pas-a-pas.jpg\" alt=\"divis\u00e3o de polin\u00f4mios passo a passo\" class=\"wp-image-752\" width=\"420\" height=\"148\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/polynome-division-pas-a-pas.jpg\" alt=\"divis\u00e3o polinomial passo a passo\" class=\"wp-image-759\" width=\"420\" height=\"134\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Como em todas as opera\u00e7\u00f5es com polin\u00f4mios, \u00e9 importante ordenar os polin\u00f4mios do grau mais alto para o grau mais baixo, de modo que todos os termos do mesmo grau estejam na mesma coluna.<\/p>\n<p> Depois de colocarmos os resultados da multiplica\u00e7\u00e3o com o sinal oposto, precisamos adicionar os termos alinhados verticalmente: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/addition-soustraction-multiplication-et-division-de-polynomes.png\" alt=\"algoritmo de divis\u00e3o polinomial\" class=\"wp-image-762\" width=\"450\" height=\"121\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Observe que ao fazer essa soma, o coeficiente de maior grau se anula e, portanto, temos um termo a menos no dividendo.<\/p>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Agora precisamos repetir o mesmo procedimento at\u00e9 que o dividendo polinomial seja um grau menor que o divisor polinomial.<\/p>\n<p> Portanto, dividimos o primeiro termo do dividendo pelo primeiro termo do divisor: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/diviser-polynomes-par-monomes.jpg\" alt=\"divis\u00e3o de polin\u00f4mios com fra\u00e7\u00f5es\" class=\"wp-image-765\" width=\"106\" height=\"61\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Colocamos o resultado no quociente: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/diviser-avec-des-polynomes.jpg\" alt=\"dividir com polin\u00f4mios\" class=\"wp-image-766\" width=\"450\" height=\"120\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Como antes, multiplicamos o novo termo do quociente por cada elemento do divisor e colocamos os resultados de sinal oposto nas colunas correspondentes do dividendo: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/diviser-deux-polynomes-par-des-polynomes-2.jpg\" alt=\"dividir polin\u00f4mios por polin\u00f4mios\" class=\"wp-image-785\" width=\"450\" height=\"157\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> E adicionamos verticalmente: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/diviser-des-fractions-de-polynomes-2.jpg\" alt=\"dividindo fra\u00e7\u00f5es de polin\u00f4mios\" class=\"wp-image-786\" width=\"450\" height=\"197\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> O polin\u00f4mio do dividendo ainda n\u00e3o \u00e9 um grau menor que o polin\u00f4mio divisor, ent\u00e3o precisamos continuar fazendo o mesmo processo.<\/p>\n<p> Ent\u00e3o primeiro dividimos o primeiro termo do dividendo pelo primeiro termo do divisor, depois multiplicamos o resultado por cada termo do divisor, depois colocamos os resultados modificados em sinal no dividendo e, por fim, somamos verticalmente: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/division-de-deux-polynomes-ou-plus-2.jpg\" alt=\"divis\u00e3o de dois ou mais polin\u00f4mios 2\" class=\"wp-image-787\" width=\"450\" height=\"269\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Ent\u00e3o j\u00e1 obtivemos que o polin\u00f4mio do dividendo \u00e9 de grau menor que o grau do divisor, pois o dividendo \u00e9 de grau 0 e o divisor \u00e9 de grau 1. Portanto, a divis\u00e3o est\u00e1 completa. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/degres-dune-division-de-polynomes-2.jpg\" alt=\"graus de uma divis\u00e3o de polin\u00f4mios\" class=\"wp-image-779\" width=\"486\" height=\"343\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> O resultado da divis\u00e3o \u00e9 portanto: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/resultat-d-une-division-de-polynomes.jpg\" alt=\"resultado da divis\u00e3o de polin\u00f4mios\" class=\"wp-image-781\" width=\"246\" height=\"86\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Por outro lado, podemos verificar que realizamos corretamente a divis\u00e3o polinomial com base na condi\u00e7\u00e3o fundamental para a divis\u00e3o de polin\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-2657eeecea1011960aa78859c32b354f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(x)=d(x) \\cdot c(x) + R(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"199\" 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-6fcec7b5468a6c0bb572121a522abbf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+4x^2+12=(x-4) \\cdot (x^2+8x+32) + 140\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"357\" 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-b75f816888653ede8543a9d100f669fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+4x^2+12=x^3+8x^2+32x-4x^2-32x-128+ 140\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"440\" style=\"vertical-align: -2px;\"><\/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-f4d7efc7a1bf11053fb42685599f5cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+4x^2+12=x^3+4x^2+12\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"234\" style=\"vertical-align: -2px;\"><\/p>\n<p> \u2705<\/p>\n<p> A equa\u00e7\u00e3o est\u00e1 satisfeita, ent\u00e3o a divis\u00e3o polinomial foi realizada corretamente.<\/p>\n<p> Para terminarmos a divis\u00e3o de polin\u00f4mios, esperamos ter ajudado voc\u00ea com esta explica\u00e7\u00e3o. O que voc\u00ea achou do m\u00e9todo de divis\u00e3o de polin\u00f4mios? Voc\u00ea tem alguma d\u00favida? Voc\u00ea gosta disso? Ou voc\u00ea preferiria que n\u00e3o existissem divis\u00f5es polinomiais? \ud83d\ude02 Lemos voc\u00ea nos coment\u00e1rios! \ud83d\udc47\ud83d\udc47\ud83d\udc47 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-de-la-division-de-polinomios\"><\/span> Propriedades da divis\u00e3o de polin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Qualquer divis\u00e3o de polin\u00f4mios atende \u00e0s seguintes caracter\u00edsticas:<\/p>\n<p> <strong><span style=\"color:#ff5733;\">\u2713<\/span><\/strong> O grau do dividendo polinomial deve ser sempre maior que o grau do divisor polinomial.<\/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-d2b2ef1b20f409f0d0dffe0311c2b415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{grado } D(x) >\\text{grado } d(x)&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;193&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p> <strong><span style=\"color:#ff5733;\">\u2713<\/span><\/strong> O grau do dividendo polinomial equivale \u00e0 soma dos graus do divisor e do quociente.<\/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-aafc5d6c5e45ff5f6ee0b0d21043650c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{grado } D(x) =\\text{grado } d(x)+\\text{grado } c(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"296\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <strong><span style=\"color:#ff5733;\">\u2713<\/span><\/strong> O grau do resto \u00e9 sempre menor que o grau do divisor (e portanto tamb\u00e9m do dividendo).<\/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-5cc6e7e89649c55e9d30a82abaf8a37b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{grado } R(x) <\\text{grado } d(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"192\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <strong><span style=\"color:#ff5733;\">\u2713<\/span><\/strong> O dividendo \u00e9 igual ao produto do divisor vezes o quociente mais o resto. Esta condi\u00e7\u00e3o tamb\u00e9m \u00e9 colocada na divis\u00e3o de n\u00fameros. <\/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-2657eeecea1011960aa78859c32b354f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(x)=d(x) \\cdot c(x) + R(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-la-division-de-polinomios\"><\/span> Exerc\u00edcios resolvidos sobre divis\u00e3o de polin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Determine o resultado da seguinte divis\u00e3o de um polin\u00f4mio por um mon\u00f4mio: <\/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-35e9fb18793954cb42af226f0a0e3935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(15x^5+9x^3 \\right) : \\left(3x^2\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"154\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para dividir um polin\u00f4mio por um mon\u00f4mio voc\u00ea deve resolver a divis\u00e3o de cada termo do polin\u00f4mio pelo referido mon\u00f4mio:<\/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-ffa558b26adc36e2ac45a842a6cf33df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\left(15x^5+9x^3 \\right) : \\left(3x^2\\right) &amp; =  \\cfrac{15x^{5}}{3x^2}+ \\cfrac{9x^3}{3x^2} \\\\[2ex] &amp; = \\bm{5x^3+3x} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"268\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Lembre-se que na divis\u00e3o entre mon\u00f4mios, os coeficientes s\u00e3o divididos entre si e os expoentes das pot\u00eancias cuja base \u00e9 a mesma s\u00e3o subtra\u00eddos.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 2<\/h3>\n<p> Calcule a seguinte divis\u00e3o de um polin\u00f4mio por um mon\u00f4mio: <\/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-1f30a614f1cf21418258b08ced9d4c3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 16x^5-4x^3-20x^2 \\right) : \\left(4x^2\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"211\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para dividir um polin\u00f4mio por um mon\u00f4mio voc\u00ea deve dividir cada termo do polin\u00f4mio pelo referido mon\u00f4mio:<\/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-868da1546d3e4d33e8226774020cbb2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\left( 16x^5-4x^3-20x^2 \\right) : \\left(4x^2\\right) &amp; =  \\cfrac{16x^5}{4x^2}+ \\cfrac{-4x^3}{4x^2} + \\cfrac{-20x^2}{4x^2} \\\\[2ex] &amp; = \\bm{4x^3-x-5} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"79\" width=\"428\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Lembre-se que na divis\u00e3o monomial os coeficientes s\u00e3o divididos entre si e os expoentes das pot\u00eancias com base equivalente s\u00e3o subtra\u00eddos.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 3<\/h3>\n<p> Resolva a seguinte divis\u00e3o de um polin\u00f4mio por um mon\u00f4mio: <\/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-1fd0d169a07a40153ad63f4f8e4ba0a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(12x^{10}-30x^7-18x^6+54x^4  \\right) : \\left(-6x^3\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"298\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para dividir um polin\u00f4mio por um mon\u00f4mio voc\u00ea deve resolver a divis\u00e3o de cada termo do polin\u00f4mio pelo referido mon\u00f4mio:<\/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-a8d5fe46b397f2f531a865e7cb0df3cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\left(12x^{10}-30x^7-18x^6+54x^4  \\right) : \\left(-6x^3\\right) &amp; =  \\cfrac{12x^{10}}{-6x^3}+ \\cfrac{-30x^{7}}{-6x^3} + \\cfrac{-18x^6}{-6x^3} + \\cfrac{54x^4}{-6x^3} \\\\[2ex] &amp; = \\bm{-2x^7+5x^4+3x^3-9x} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"594\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Tenha em mente que o mon\u00f4mio divisor \u00e9 negativo e, portanto, os sinais de todas as divis\u00f5es mudam.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 4<\/h3>\n<p> Execute a seguinte divis\u00e3o dos polin\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-459044ab33c7382f69a6251d5f09fa71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^4+x^3-x^2+x+1}{x^3-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"160\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para dividir polin\u00f4mios voc\u00ea deve aplicar o m\u00e9todo explicado acima: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemples-de-division-de-polynomes.jpg\" alt=\"exemplos de divis\u00f5es polinomiais\" class=\"wp-image-798\" width=\"483\" height=\"175\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> O resultado da divis\u00e3o entre os dois polin\u00f4mios \u00e9, portanto:<\/p>\n<p class=\"has-text-align-center\"> Quociente:<\/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-cc79ac27a4802ea8e5f0a37a6889212b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> Descansar: <\/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-86c972d4f666d78aa0caa96bce5e0003_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x^2+6x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"102\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 5<\/h3>\n<p> Calcule a seguinte divis\u00e3o de polin\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-ff119dac6918e0daa7af247ccf97f4f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2x^3-3x^2-5x-5}{x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"147\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para resolver a divis\u00e3o do polin\u00f4mio pelo bin\u00f4mio devemos aplicar o m\u00e9todo que vimos acima: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-resolus-pas-a-pas-de-division-de-polynomes.png\" alt=\"exerc\u00edcios resolvidos passo a passo para a divis\u00e3o de polin\u00f4mios\" class=\"wp-image-799\" width=\"466\" height=\"240\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> O resultado da divis\u00e3o polinomial \u00e9, portanto:<\/p>\n<p class=\"has-text-align-center\"> Quociente:<\/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-ae37fa4e1a18724aca2a10c9ec7f7230_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x^2+x-3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> Descansar: <\/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-2981688f5b26fd15fa08c897afa741ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-11\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 6<\/h3>\n<p> Resolva a seguinte divis\u00e3o de polin\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-f864673bfbdbe68cb2c6df50c72c57bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^4+x^2+3}{x^3+3x^2+2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"107\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para calcular a divis\u00e3o de polin\u00f4mios, devemos aplicar o m\u00e9todo explicado: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-division-de-2-polynomes.png\" alt=\"exemplo de divis\u00e3o de 2 polin\u00f4mios\" class=\"wp-image-804\" width=\"485\" height=\"177\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> O resultado da divis\u00e3o entre os dois polin\u00f4mios \u00e9, portanto:<\/p>\n<p class=\"has-text-align-center\"> Quociente:<\/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-193c295d8fc62eac0984aa4fc668bf9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> Descansar: <\/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-46cbad1fed9a167108eda3fcea052e57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^2+6x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 7<\/h3>\n<p> Encontre o resultado da seguinte divis\u00e3o entre 2 polin\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-988beca7ee36a80a9eb563823d0a961c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x^4-2x^3+x^2-x-3}{x^2+x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"168\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para calcular a divis\u00e3o do polin\u00f4mio pelo trin\u00f4mio deve-se aplicar o m\u00e9todo explicado: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/diviser-polynomes-exercices.png\" alt=\"exerc\u00edcios resolvidos passo a passo para dividir polin\u00f4mios\" class=\"wp-image-808\" width=\"505\" height=\"235\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> O resultado da divis\u00e3o entre os dois polin\u00f4mios \u00e9, portanto:<\/p>\n<p class=\"has-text-align-center\"> Quociente:<\/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-9be39dcfede62d2ebf9b02252a7f256f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-3x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> Descansar: <\/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-3af87296ebec1f7c956d957453aa3abb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x-6\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"54\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> \ud83d\udc49\ud83d\udc49\ud83d\udc49Se voc\u00ea chegou at\u00e9 aqui, significa que j\u00e1 sabe como os polin\u00f4mios s\u00e3o divididos. Brilhante! Agora que voc\u00ea j\u00e1 domina a divis\u00e3o de polin\u00f4mios, saiba que existe um m\u00e9todo que permite <span style=\"text-decoration: underline;\">resolver certas divis\u00f5es entre polin\u00f4mios com muito mais rapidez<\/span> . Esta \u00e9 <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/regras-resolvidas-exemplos-exercicios-ruffini\/\">uma divis\u00e3o sint\u00e9tica ou regra de Ruffini<\/a><\/span><\/strong> , voc\u00ea pode ver como esse truque \u00e9 aplicado e quando pode ser usado clicando no link.\ud83d\ude09<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea descobrir\u00e1 como dividir polin\u00f4mios, tanto a divis\u00e3o de um polin\u00f4mio por um mon\u00f4mio quanto a divis\u00e3o de um polin\u00f4mio por outro polin\u00f4mio. Voc\u00ea tamb\u00e9m poder\u00e1 ver exemplos de divis\u00e3o de polin\u00f4mios e praticar exerc\u00edcios resolvidos passo a passo. Al\u00e9m disso, voc\u00ea encontrar\u00e1 as propriedades desta opera\u00e7\u00e3o polinomial. Divis\u00e3o polinomial (ou polinomial) Antes &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/divisao-de-polinomios-exemplos-exercicios-resolvidos-dividir\/\"> <span class=\"screen-reader-text\">Divis\u00e3o polinomial<\/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-54","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>\u25b7 Como dividir polin\u00f4mios (exerc\u00edcios resolvidos)<\/title>\n<meta name=\"description\" content=\"Explica\u00e7\u00e3o passo a passo de como dividir polin\u00f4mios. 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