{"id":280,"date":"2023-07-06T21:57:21","date_gmt":"2023-07-06T21:57:21","guid":{"rendered":"https:\/\/mathority.org\/pt\/soma-de-polinomios-exemplos-adicao-de-exercicios-resolvidos\/"},"modified":"2023-07-06T21:57:21","modified_gmt":"2023-07-06T21:57:21","slug":"soma-de-polinomios-exemplos-adicao-de-exercicios-resolvidos","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/soma-de-polinomios-exemplos-adicao-de-exercicios-resolvidos\/","title":{"rendered":"Adi\u00e7\u00e3o de polin\u00f4mios"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o de como \u00e9 feita a adi\u00e7\u00e3o de polin\u00f4mios. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos de somas de polin\u00f4mios e at\u00e9 exerc\u00edcios resolvidos passo a passo. Por fim, explicamos tamb\u00e9m quais s\u00e3o as propriedades deste tipo de opera\u00e7\u00e3o com polin\u00f4mios. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFComo-se-hace-la-suma-de-polinomios\"><\/span> Como adicionar polin\u00f4mios?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Em matem\u00e1tica, para adicionar dois ou mais polin\u00f4mios, os termos dos polin\u00f4mios que s\u00e3o semelhantes devem ser somados. Ou seja, somar polin\u00f4mios consiste em somar termos que possuem a mesma parte literal (mesmas vari\u00e1veis e mesmos expoentes).<\/strong><\/p>\n<p> Assim, uma soma de polin\u00f4mios pode ser feita de duas maneiras diferentes: com o m\u00e9todo vertical ou com o m\u00e9todo horizontal. Abaixo est\u00e1 a explica\u00e7\u00e3o de ambos os procedimentos, mas aconselhamos que voc\u00ea aprenda primeiro como adicionar polin\u00f4mios verticalmente e depois passe para o m\u00e9todo horizontal. Obviamente fique com o que voc\u00ea preferir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Suma-de-polinomios-vertical\"><\/span> Adicionando polin\u00f4mios verticais<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A seguir, veremos como dois polin\u00f4mios s\u00e3o adicionados verticalmente usando um exemplo:<\/p>\n<ul>\n<li> Adicione os dois polin\u00f4mios a seguir:<\/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-b91dccc42a00d2b708bab366394a5f09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 6x^4+4x^3+2x-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-b1e8679a7a0fc9ce7d7e4a3734424d44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = 3x^4-7x^3+6x^2-4x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"255\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A primeira coisa que precisamos fazer \u00e9 colocar um polin\u00f4mio abaixo do outro, de modo que os termos semelhantes dos dois polin\u00f4mios fiquem alinhados por colunas: <\/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\/somme-de-polynomes-exemples.jpg\" alt=\"exemplos de adi\u00e7\u00e3o de polin\u00f4mios\" class=\"wp-image-442\" width=\"340\" height=\"82\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-background\" style=\"background-color:#fffde7\"> <strong>Aten\u00e7\u00e3o:<\/strong> Se um polin\u00f4mio n\u00e3o possuir termo de determinado grau, o espa\u00e7o deve ser deixado vazio. Por exemplo<\/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-a02128e5beebe26f72d5c019c15c8744_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=6x^4+4x^3+2x-3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<p> Voc\u00ea n\u00e3o possui um mon\u00f4mio de grau 2, por isso h\u00e1 um espa\u00e7o vazio em seu site. <\/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\/ajouter-des-polynomes.jpg\" alt=\"adi\u00e7\u00e3o de polin\u00f4mios\" class=\"wp-image-4065\" width=\"341\" height=\"123\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Depois de colocar todos os termos em ordem do grau mais alto para o mais baixo, adicionamos os coeficientes em cada coluna mantendo as partes literais iguais: <\/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\/somme-de-polynomes.jpg\" alt=\"soma de polin\u00f4mios\" class=\"wp-image-451\" width=\"352\" height=\"130\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Consequentemente, o resultado obtido da soma dos 2 polin\u00f4mios \u00e9:<\/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-82730f8268524f049c09b22e288365f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P(x)+Q(x) = 9x^4-3x^3+6x^2-2x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"315\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Agora que voc\u00ea entende a adi\u00e7\u00e3o de polin\u00f4mios, saiba que tamb\u00e9m \u00e9 poss\u00edvel somar fra\u00e7\u00f5es formadas por polin\u00f4mios. Este tipo de opera\u00e7\u00e3o \u00e9 chamada de <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/fracoes-algebricas-operacoes-simplificadas-adicao-subtracao-multiplicacao-divisao-exercicios-resolvidos\/\">adi\u00e7\u00e3o de fra\u00e7\u00f5es alg\u00e9bricas<\/a><\/span><\/strong> . Clique neste link e aprenda n\u00e3o apenas como s\u00e3o calculadas as somas das fra\u00e7\u00f5es alg\u00e9bricas, mas tamb\u00e9m como s\u00e3o resolvidas todas as opera\u00e7\u00f5es com fra\u00e7\u00f5es alg\u00e9bricas. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Suma-de-polinomios-horizontal\"><\/span>Adi\u00e7\u00e3o horizontal de polin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Acabamos de ver como adicionar polin\u00f4mios verticalmente, mas agora veremos o outro m\u00e9todo para adicionar polin\u00f4mios: adicionar polin\u00f4mios horizontalmente. Certamente este procedimento \u00e9 mais r\u00e1pido que o anterior, por\u00e9m \u00e9 necess\u00e1rio ter um dom\u00ednio maior dos conceitos de polin\u00f4mios.<\/p>\n<p> Ent\u00e3o vamos ver em que consiste esse m\u00e9todo de somar polin\u00f4mios por meio de um exemplo. E para que voc\u00ea possa ver as diferen\u00e7as entre os dois m\u00e9todos, adicionaremos os mesmos polin\u00f4mios do exemplo anterior:<\/p>\n<ul>\n<li> Calcule a soma dos dois polin\u00f4mios a seguir:<\/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-b91dccc42a00d2b708bab366394a5f09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 6x^4+4x^3+2x-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-b1e8679a7a0fc9ce7d7e4a3734424d44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = 3x^4-7x^3+6x^2-4x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"255\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Voc\u00ea deve primeiro posicionar os dois polin\u00f4mios na mesma opera\u00e7\u00e3o, ou seja, um ap\u00f3s o outro: <\/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-faire-une-somme-de-polynomes.jpg\" alt=\"como somar polin\u00f4mios\" class=\"wp-image-461\" width=\"539\" height=\"38\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> E agora somamos os termos que possuem partes literais id\u00eanticas, ou seja, os termos com as mesmas vari\u00e1veis (letras) e os mesmos expoentes. Termos que n\u00e3o sejam semelhantes n\u00e3o podem ser adicionados. <\/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\/somme-de-polynomes-horizontal.jpg\" alt=\"soma horizontal de polin\u00f4mios\" class=\"wp-image-462\" width=\"525\" height=\"272\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> O polin\u00f4mio resultante da adi\u00e7\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\/ajouter-des-polynomes-1.jpg\" alt=\"como adicionar polin\u00f4mios\" class=\"wp-image-460\" width=\"311\" height=\"42\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Como voc\u00ea pode ver, obtivemos o mesmo resultado com ambos os m\u00e9todos, portanto, ao adicionar polin\u00f4mios voc\u00ea pode usar o que melhor lhe convier. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-la-suma-de-polinomios\"><\/span> Problemas resolvidos de adi\u00e7\u00e3o de polin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para que voc\u00ea possa praticar, deixamos v\u00e1rios exerc\u00edcios resolvidos de somas de polin\u00f4mios. Se voc\u00ea tiver alguma d\u00favida, pode perguntar nos coment\u00e1rios da p\u00e1gina e responderemos o mais breve poss\u00edvel.<\/p>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Adicione os dois polin\u00f4mios 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-c66460c618b4b6ac0bb557f7571e5cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 3x^3-5x^2+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-a6b6edd4928e50aa5f8fdf28ef103ad5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = 4x^3+x^2-9x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/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 solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Neste caso, adicionaremos os dois polin\u00f4mios verticalmente. Para fazer isso, ordenamos os polin\u00f4mios por grau e somamos os mon\u00f4mios localizados na mesma coluna: <\/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-de-sommes-de-polynomes.jpg\" alt=\"exerc\u00edcios resolvidos de somas de polin\u00f4mios\" class=\"wp-image-470\" width=\"244\" height=\"113\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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> Resolva a soma dos dois polin\u00f4mios 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-d45a0dc63962f707547e64711acbcbc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = 8x^4+2x^3+9x^2-3x-7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"256\" 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-fb36b7a4150d95e12b3b7b4f7270aece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = 5x^4+6x^3-4x+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" style=\"vertical-align: -5px;\"><\/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 solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Somaremos os dois polin\u00f4mios usando o m\u00e9todo vertical. Portanto, ordenamos os polin\u00f4mios por grau e somamos os termos localizados na mesma coluna: <\/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-de-polynomes-add.jpg\" alt=\"adi\u00e7\u00e3o de polin\u00f4mios\" class=\"wp-image-476\" width=\"315\" height=\"114\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> Observe que neste caso particular, deve-se deixar um espa\u00e7o em branco na coluna de grau 2 do segundo polin\u00f4mio, pois n\u00e3o possui termo quadr\u00e1tico.<\/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> Qual \u00e9 a soma dos dois polin\u00f4mios 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-4c9b88d8da1ef9698949ce338e5db355_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) = -3x^5+4x^4-2x^3-6x^2+2x-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"318\" 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-dc1d03704e9cedd2daa6594d6636970c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) = 6x^5-7x^4+8x^3-3x^2-6x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"304\" style=\"vertical-align: -5px;\"><\/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 solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Realizaremos a adi\u00e7\u00e3o dos dois polin\u00f4mios usando o m\u00e9todo vertical. ENT\u00c3O: <\/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\/exercice-resolu-etape-par-etape-de-sommes-de-polynomes.jpg\" alt=\"exerc\u00edcio resolvido passo a passo somas de polin\u00f4mios\" class=\"wp-image-478\" width=\"389\" height=\"113\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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> Calcule a soma dos tr\u00eas polin\u00f4mios 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-710d013a260a4cda93f02609c782fe2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x) =6x^4-3x^3+8x^2+4x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"255\" 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-3ee9369da6e4374ca5da7dd346c2b9b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q(x) =-9x^4+5x^3+6x^2-2x+7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"270\" 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-30a82581e496ee677f90a7adb7a2bd6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"R(x) =-4x^4+6x^3-9x^2+6x-3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"270\" style=\"vertical-align: -5px;\"><\/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 solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Calcularemos a soma dos 3 polin\u00f4mios usando o m\u00e9todo vertical. Colocamos, portanto, os polin\u00f4mios ordenados por grau e somamos os termos localizados na mesma coluna: <\/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\/somme-de-3-polynomes.jpg\" alt=\"soma de 3 polin\u00f4mios diferentes\" class=\"wp-image-483\" width=\"341\" height=\"151\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> \ud83d\udc49\ud83d\udc49\ud83d\udc49Agora que voc\u00ea viu como dois polin\u00f4mios se somam, voc\u00ea pode estar interessado em outra opera\u00e7\u00e3o caracter\u00edstica dos polin\u00f4mios: o fator comum. Extrair um fator comum de um polin\u00f4mio \u00e9 bastante complicado (e dif\u00edcil de entender); na verdade, muitos erros s\u00e3o cometidos ao fazer isso. Por isso preparamos um guia onde explicamos passo a passo como <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/extrair-extrair-exercicios-exemplos-resolvidos-de-fator-comum\/\">extrair o fator comum<\/a><\/span><\/strong> , para que voc\u00ea entenda perfeitamente e n\u00e3o cometa erros ao fazer esta opera\u00e7\u00e3o. Descubra quais s\u00e3o as <span style=\"text-decoration: underline;\">dicas para extrair o fator comum de um polin\u00f4mio<\/span> clicando no link. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-de-la-suma-de-polinomios\"><\/span> Propriedades de adi\u00e7\u00e3o de polin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A soma dos polin\u00f4mios possui as seguintes caracter\u00edsticas:<\/p>\n<ul>\n<li> <strong>Propriedade associativa<\/strong> : Ao adicionar 3 ou mais polin\u00f4mios, n\u00e3o importa como os polin\u00f4mios s\u00e3o agrupados porque o resultado \u00e9 sempre o mesmo. Ou seja, verifica-se a seguinte igualdade:<\/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-d7783308b5217209a869a9990fe254a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl(P(x)+Q(x)\\bigr)+R(x) = P(x)+\\bigl(Q(x)+R(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"365\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Propriedade comutativa<\/strong> : na adi\u00e7\u00e3o de polin\u00f4mios a ordem das adi\u00e7\u00f5es n\u00e3o modifica o resultado da adi\u00e7\u00e3o.<\/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-c48e1b8f3762f6b2105c3623fad05789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)+Q(x)= Q(x)+P(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Elemento neutro<\/strong> : Obviamente, adicionar um polin\u00f4mio mais qualquer outro polin\u00f4mio com valor num\u00e9rico zero \u00e9 equivalente ao primeiro 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-a2d5581ec2ffccb80bbddec261d421ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)+0=P(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Elemento oposto<\/strong> : O resultado da adi\u00e7\u00e3o de qualquer polin\u00f4mio mais seu polin\u00f4mio oposto \u00e9 sempre 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-d82cd6d40b9041819faec5592980a8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)+\\bigl(-P(x)\\bigr)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"160\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> O que voc\u00ea acha da explica\u00e7\u00e3o? Voc\u00ea achou isso \u00fatil? Qual m\u00e9todo de adi\u00e7\u00e3o de polin\u00f4mios voc\u00ea prefere, vertical ou horizontal? N\u00f3s lemos voc\u00ea nos coment\u00e1rios! \ud83d\udc40<\/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 encontrar\u00e1 a explica\u00e7\u00e3o de como \u00e9 feita a adi\u00e7\u00e3o de polin\u00f4mios. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos de somas de polin\u00f4mios e at\u00e9 exerc\u00edcios resolvidos passo a passo. Por fim, explicamos tamb\u00e9m quais s\u00e3o as propriedades deste tipo de opera\u00e7\u00e3o com polin\u00f4mios. Como adicionar polin\u00f4mios? Em matem\u00e1tica, para adicionar dois ou mais &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/soma-de-polinomios-exemplos-adicao-de-exercicios-resolvidos\/\"> <span class=\"screen-reader-text\">Adi\u00e7\u00e3o de polin\u00f4mios<\/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-280","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>Adicionando polin\u00f4mios - Mathority<\/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\/soma-de-polinomios-exemplos-adicao-de-exercicios-resolvidos\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Adicionando polin\u00f4mios - Mathority\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 a explica\u00e7\u00e3o de como \u00e9 feita a adi\u00e7\u00e3o de polin\u00f4mios. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos de somas de polin\u00f4mios e at\u00e9 exerc\u00edcios resolvidos passo a passo. Por fim, explicamos tamb\u00e9m quais s\u00e3o as propriedades deste tipo de opera\u00e7\u00e3o com polin\u00f4mios. Como adicionar polin\u00f4mios? 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