{"id":1807676,"date":"2026-10-22T14:27:00","date_gmt":"2026-10-22T17:27:00","guid":{"rendered":"https:\/\/concursos.estrategia.com\/portal\/?p=1807676"},"modified":"2026-09-30T14:16:50","modified_gmt":"2026-09-30T17:16:50","slug":"polinomios","status":"publish","type":"post","link":"https:\/\/concursos.estrategia.com\/portal\/polinomios\/","title":{"rendered":"Polin\u00f4mios"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Aprenda os conceitos essenciais para resolu\u00e7\u00e3o de quest\u00f5es sobre polin\u00f4mios com um resumo para as principais provas de concursos.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"681\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/04\/28110618\/blackboard-inscribed-with-scientific-formulas-calculations-1-1024x681.jpg\" alt=\"Quadro negro com f\u00f3rmulas matem\u00e1ticas - polin\u00f4mios\" class=\"wp-image-1758240\" style=\"aspect-ratio:1.503671713823598;width:609px;height:auto\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/04\/28110618\/blackboard-inscribed-with-scientific-formulas-calculations-1-1024x681.jpg 1024w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/04\/28110618\/blackboard-inscribed-with-scientific-formulas-calculations-1-300x200.jpg 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/04\/28110618\/blackboard-inscribed-with-scientific-formulas-calculations-1-768x511.jpg 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/04\/28110618\/blackboard-inscribed-with-scientific-formulas-calculations-1-1536x1022.jpg 1536w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/04\/28110618\/blackboard-inscribed-with-scientific-formulas-calculations-1-2048x1363.jpg 2048w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2026\/04\/28110618\/blackboard-inscribed-with-scientific-formulas-calculations-1-150x100.jpg 150w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ol\u00e1, pessoal! Tudo bem com voc\u00eas?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As express\u00f5es alg\u00e9bricas est\u00e3o presentes em diversos conte\u00fados da Matem\u00e1tica e permitem representar rela\u00e7\u00f5es entre quantidades conhecidas e desconhecidas. Dentro desse universo, os <strong>polin\u00f4mios<\/strong> ocupam uma posi\u00e7\u00e3o de destaque, pois servem de base para o estudo de equa\u00e7\u00f5es, fun\u00e7\u00f5es, fatora\u00e7\u00e3o, produtos not\u00e1veis e diversos outros assuntos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Embora muitas quest\u00f5es apresentem apenas opera\u00e7\u00f5es alg\u00e9bricas, \u00e9 importante compreender a estrutura dessas express\u00f5es. Identificar coeficientes, termos semelhantes e o grau de um polin\u00f4mio, por exemplo, pode tornar os c\u00e1lculos muito mais simples e evitar erros durante a resolu\u00e7\u00e3o.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Em provas de bancas como <strong><\/strong><strong><a href=\"https:\/\/conhecimento.fgv.br\/concursos\" target=\"_blank\" rel=\"noreferrer noopener\">FGV<\/a>, <a href=\"https:\/\/www.concursosfcc.com.br\/\" target=\"_blank\" rel=\"noreferrer noopener\">FCC<\/a><\/strong> <strong>e<\/strong> <a href=\"https:\/\/www.cebraspe.org.br\/concursos\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Cebraspe<\/strong><\/a>, os polin\u00f4mios podem aparecer diretamente em quest\u00f5es de simplifica\u00e7\u00e3o e opera\u00e7\u00f5es ou, ainda, como ferramenta necess\u00e1ria para resolver problemas envolvendo \u00e1reas, valores desconhecidos e outras situa\u00e7\u00f5es contextualizadas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Neste artigo, estudaremos os principais conceitos relacionados aos <strong>polin\u00f4mios<\/strong>, come\u00e7ando pelos mon\u00f4mios e avan\u00e7ando para as opera\u00e7\u00f5es alg\u00e9bricas e exemplos semelhantes aos encontrados em provas de concursos p\u00fablicos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Confira os t\u00f3picos que ser\u00e3o abordados:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mon\u00f4mios;<\/li>\n\n\n\n<li>Polin\u00f4mios;<\/li>\n\n\n\n<li>Opera\u00e7\u00f5es com polin\u00f4mios;<\/li>\n\n\n\n<li>Exemplos resolvidos;<\/li>\n\n\n\n<li>Resumo.<\/li>\n<\/ul>\n\n\n\n<h2 id=\"h-monomios\" class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\">Mon\u00f4mios<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Um <strong>mon\u00f4mio<\/strong> \u00e9 uma express\u00e3o alg\u00e9brica formada pelo produto entre um n\u00famero e uma ou mais vari\u00e1veis elevadas a expoentes inteiros n\u00e3o negativos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por exemplo:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>5x\u00b2<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00e9 um mon\u00f4mio, assim como:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>\u22123xy\u00b3<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">No mon\u00f4mio 5x\u00b2, podemos identificar duas partes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>coeficiente:<\/strong> 5;<\/li>\n\n\n\n<li><strong>parte literal:<\/strong> x\u00b2.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">J\u00e1 em \u22123xy\u00b3, o coeficiente \u00e9 \u22123 e a parte literal \u00e9 xy\u00b3.<\/p>\n\n\n\n<h3 id=\"h-grau-de-um-monomio\" class=\"wp-block-heading\"><strong>Grau de um mon\u00f4mio<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">O grau de um mon\u00f4mio corresponde \u00e0 <strong>soma dos expoentes de suas vari\u00e1veis<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por exemplo: 7x\u00b3 possui grau 3.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">J\u00e1 4x\u00b2y\u00b3 possui grau: 2 + 3 = 5.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Al\u00e9m disso, uma constante diferente de zero, como 8, pode ser considerada um mon\u00f4mio de grau zero.<\/p>\n\n\n\n<h3 id=\"h-monomios-semelhantes\" class=\"wp-block-heading\"><strong>Mon\u00f4mios semelhantes<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Dois ou mais mon\u00f4mios s\u00e3o <strong>semelhantes quando possuem exatamente a mesma parte literal<\/strong>, ou seja, as mesmas vari\u00e1veis elevadas aos mesmos expoentes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por exemplo: 3x\u00b2 e 7x\u00b2 s\u00e3o semelhantes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por\u00e9m, 3x\u00b2 e 7x\u00b3 n\u00e3o s\u00e3o semelhantes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Da mesma forma, 5xy\u00b2 e \u22122xy\u00b2 s\u00e3o semelhantes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Essa identifica\u00e7\u00e3o ser\u00e1 fundamental para realizar somas e subtra\u00e7\u00f5es entre <strong>polin\u00f4mios<\/strong>.<\/p>\n\n\n\n<h2 id=\"h-polinomios\" class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\"><strong>Polin\u00f4mios<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Um polin\u00f4mio \u00e9 uma express\u00e3o alg\u00e9brica formada pela soma ou subtra\u00e7\u00e3o de mon\u00f4mios.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Considere:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>P(x) = 3x\u00b3 \u2212 2x\u00b2 + 5x \u2212 7<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Nesse caso, temos quatro termos:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">3x\u00b3, \u22122x\u00b2, 5x e \u22127.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Os n\u00fameros 3, \u22122, 5 e \u22127 s\u00e3o os <strong>coeficientes<\/strong> do polin\u00f4mio.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">O termo \u22127, que n\u00e3o possui vari\u00e1vel, \u00e9 denominado <strong>termo independente<\/strong>.<\/p>\n\n\n\n<h3 id=\"h-grau-dos-polinomios\" class=\"wp-block-heading\"><strong>Grau dos polin\u00f4mios<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">O grau de um polin\u00f4mio n\u00e3o nulo corresponde ao <strong>maior grau<\/strong> entre seus mon\u00f4mios depois que a express\u00e3o est\u00e1 simplificada.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por exemplo: P(x) = 2x\u2074 \u2212 3x\u00b2 + x \u2013 8 possui grau <strong>4<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">J\u00e1 Q(x) = 5x\u00b2 + 7x \u2013 1 possui grau <strong>2<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c9 importante observar que o grau deve ser determinado ap\u00f3s a redu\u00e7\u00e3o dos termos semelhantes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por exemplo:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">P(x) = 4x\u00b3 \u2212 4x\u00b3 + 2x\u00b2 + 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Os termos de terceiro grau se anulam. Assim:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">P(x) = 2x\u00b2 + 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Logo, o polin\u00f4mio possui <strong>grau 2<\/strong>, e n\u00e3o grau 3.<\/p>\n\n\n\n<h3 id=\"h-classificacao-pelo-numero-de-termos\" class=\"wp-block-heading\"><strong>Classifica\u00e7\u00e3o pelo n\u00famero de termos<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Algumas express\u00f5es recebem nomes espec\u00edficos conforme a quantidade de termos:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>mon\u00f4mio:<\/strong> um termo;<\/li>\n\n\n\n<li><strong>bin\u00f4mio:<\/strong> dois termos;<\/li>\n\n\n\n<li><strong>trin\u00f4mio:<\/strong> tr\u00eas termos.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Por exemplo: 3x + 2 \u00e9 um bin\u00f4mio, enquanto x\u00b2 + 5x + 6 \u00e9 um trin\u00f4mio.<\/p>\n\n\n\n<h3 id=\"h-valor-numerico-dos-polinomios\" class=\"wp-block-heading\"><strong>Valor num\u00e9rico dos polin\u00f4mios<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Tamb\u00e9m podemos determinar o valor num\u00e9rico de um polin\u00f4mio substituindo a vari\u00e1vel por determinado n\u00famero.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Considere:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">P(x) = 2x\u00b2 \u2212 3x + 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para x = 2:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">P(2) = 2\u00b72\u00b2 \u2212 3\u00b72 + 4<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">P(2) = 8 \u2212 6 + 4<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>P(2) = 6<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Esse procedimento aparece com frequ\u00eancia em quest\u00f5es envolvendo <strong>polin\u00f4mios<\/strong>, al\u00e9m de ser fundamental em assuntos como Teorema do Resto.<\/p>\n\n\n\n<h2 id=\"h-operacoes-com-polinomios\" class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\">Opera\u00e7\u00f5es Com Polin\u00f4mios<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">As principais opera\u00e7\u00f5es com <strong>polin\u00f4mios<\/strong> seguem as propriedades usuais da \u00e1lgebra. Contudo, \u00e9 necess\u00e1rio prestar aten\u00e7\u00e3o aos termos semelhantes e aos expoentes das vari\u00e1veis.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Uma boa estrat\u00e9gia \u00e9 organizar os termos em ordem decrescente de grau antes de realizar as opera\u00e7\u00f5es.<\/p>\n\n\n\n<h3 id=\"h-1-soma\" class=\"wp-block-heading\"><strong>1) Soma<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Na soma, devemos juntar os termos semelhantes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Considere:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(x) = 3x\u00b2 + 2x + 5<\/li>\n\n\n\n<li>Q(x) = 4x\u00b2 \u2212 x + 3<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">P(x) + Q(x)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">= 3x\u00b2 + 2x + 5 + 4x\u00b2 \u2212 x + 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Agrupando os termos semelhantes:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>=<\/strong> <strong>7x\u00b2 + x + 8<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Portanto, <strong>somamos apenas os coeficientes dos termos que possuem a mesma parte literal<\/strong>.<\/p>\n\n\n\n<h3 id=\"h-2-subtracao\" class=\"wp-block-heading\"><strong>2) Subtra\u00e7\u00e3o<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Na subtra\u00e7\u00e3o, devemos ter aten\u00e7\u00e3o especial aos sinais.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Considere:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(x) = 5x\u00b2 + 3x \u2212 2<\/li>\n\n\n\n<li>Q(x) = 2x\u00b2 \u2212 4x + 1<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">P(x) \u2212 Q(x)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">= 5x\u00b2 + 3x \u2212 2 \u2212 (2x\u00b2 \u2212 4x + 1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Distribuindo o sinal negativo:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">= 5x\u00b2 + 3x \u2212 2 \u2212 2x\u00b2 + 4x \u2212 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Logo:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>=<\/strong> <strong>3x\u00b2 + 7x \u2212 3<\/strong><\/p>\n\n\n\n<h3 id=\"h-3-multiplicacao\" class=\"wp-block-heading\"><strong>3) Multiplica\u00e7\u00e3o<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Na multiplica\u00e7\u00e3o, utilizamos a propriedade distributiva.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Considere:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">2x(x\u00b2 + 3x \u2212 4)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Multiplicando o 2x por cada termo dentro do par\u00eanteses:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">= 2x\u00b3 + 6x\u00b2 \u2212 8x<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Portanto:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>2x(x\u00b2 + 3x \u2212 4) = 2x\u00b3 + 6x\u00b2 \u2212 8x<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Quando multiplicamos dois polin\u00f4mios, cada termo do primeiro deve multiplicar todos os termos do segundo.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por exemplo:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">(x + 2)(x + 3)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">= x\u00b2 + 3x + 2x + 6<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>=<\/strong> <strong>x\u00b2 + 5x + 6<\/strong><\/p>\n\n\n\n<h3 id=\"h-4-divisao-por-monomio\" class=\"wp-block-heading\"><strong>4) Divis\u00e3o por mon\u00f4mio<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Quando um polin\u00f4mio \u00e9 dividido por um mon\u00f4mio, podemos dividir cada termo separadamente.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Considere:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">(6x\u00b3 + 9x\u00b2 \u2212 3x)\/(3x)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dividindo termo a termo:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">6x\u00b3\/(3x) + 9x\u00b2\/(3x) \u2212 3x\/(3x)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>=<\/strong> <strong>2x\u00b2 + 3x \u2212 1<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Contudo, a divis\u00e3o geral entre polin\u00f4mios exige um procedimento espec\u00edfico e costuma ser estudada separadamente.<\/p>\n\n\n\n<h2 id=\"h-exemplos-resolvidos\" class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\">Exemplos Resolvidos<\/h2>\n\n\n\n<h3 id=\"h-exemplo-1\" class=\"wp-block-heading\"><strong>Exemplo 1<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Simplifique:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">(4x\u00b2 + 3x \u2212 5) + (2x\u00b2 \u2212 7x + 8)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Resolu\u00e7\u00e3o:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Na soma de polin\u00f4mios, apenas termos semelhantes podem ser reduzidos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Agrupando os termos semelhantes:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">(4x\u00b2 + 2x\u00b2) + (3x \u2212 7x) + (\u22125 + 8)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">= <strong>6x\u00b2 \u2212 4x + 3<\/strong><\/p>\n\n\n\n<h3 id=\"h-exemplo-2\" class=\"wp-block-heading\"><strong>Exemplo 2<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Um terreno retangular possui comprimento igual a (x + 5) metros e largura igual a (x + 2) metros. Qual polin\u00f4mio representa sua \u00e1rea?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Resolu\u00e7\u00e3o:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u00e1rea de um ret\u00e2ngulo \u00e9 dada pelo produto entre comprimento e largura:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">A = (x + 5)(x + 2)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicando a distributiva:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">A = x\u00b2 + 2x + 5x + 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Logo:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>A = x\u00b2 + 7x + 10<\/strong><\/p>\n\n\n\n<h3 id=\"h-exemplo-3\" class=\"wp-block-heading\"><strong>Exemplo 3<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">O custo de produ\u00e7\u00e3o de uma empresa \u00e9 representado por:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">C(x) = 2x\u00b2 + 5x + 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">e sua receita por:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">R(x) = 5x\u00b2 + 8x + 25.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sabendo que o lucro \u00e9 dado pela diferen\u00e7a entre receita e custo, determine o polin\u00f4mio L(x) que representa o lucro.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Resolu\u00e7\u00e3o:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Temos:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">L(x) = R(x) \u2212 C(x)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Assim:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">L(x) = (5x\u00b2 + 8x + 25) \u2212 (2x\u00b2 + 5x + 10)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Distribuindo o sinal negativo:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">L(x) = 5x\u00b2 + 8x + 25 \u2212 2x\u00b2 \u2212 5x \u2212 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reduzindo os termos semelhantes:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>L(x) = 3x\u00b2 + 3x + 15<\/strong><\/p>\n\n\n\n<h2 id=\"h-resumo-polinomios\" class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\">Resumo &#8211; Polin\u00f4mios<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Para te ajudar a revisar, de forma r\u00e1pida e estrat\u00e9gia, tudo o que vimos at\u00e9 aqui, preparamos um resumo.<strong><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Conceito<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>Caracter\u00edstica<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>Exemplo<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Mon\u00f4mio<\/td><td class=\"has-text-align-center\" data-align=\"center\">Um \u00fanico termo alg\u00e9brico<\/td><td class=\"has-text-align-center\" data-align=\"center\">3x\u00b2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Termos semelhantes<\/td><td class=\"has-text-align-center\" data-align=\"center\">Mesma parte literal<\/td><td class=\"has-text-align-center\" data-align=\"center\">2x\u00b2 e 5x\u00b2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Polin\u00f4mio<\/td><td class=\"has-text-align-center\" data-align=\"center\">Soma ou subtra\u00e7\u00e3o de mon\u00f4mios<\/td><td class=\"has-text-align-center\" data-align=\"center\">x\u00b2 + 3x \u2212 2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Grau<\/td><td class=\"has-text-align-center\" data-align=\"center\">Maior grau ap\u00f3s simplifica\u00e7\u00e3o<\/td><td class=\"has-text-align-center\" data-align=\"center\">3x\u2074 + x \u2192 grau 4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Valor num\u00e9rico<\/td><td class=\"has-text-align-center\" data-align=\"center\">Substituir a vari\u00e1vel<\/td><td class=\"has-text-align-center\" data-align=\"center\">P(2)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Soma e subtra\u00e7\u00e3o<\/td><td class=\"has-text-align-center\" data-align=\"center\">Operar termos semelhantes<\/td><td class=\"has-text-align-center\" data-align=\"center\">3x + 2x = 5x<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Multiplica\u00e7\u00e3o<\/td><td class=\"has-text-align-center\" data-align=\"center\">Aplicar a distributiva<\/td><td class=\"has-text-align-center\" data-align=\"center\">x(x + 2)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Divis\u00e3o por mon\u00f4mio<\/td><td class=\"has-text-align-center\" data-align=\"center\">Dividir termo a termo<\/td><td class=\"has-text-align-center\" data-align=\"center\">6x\u00b2\/(2x) = 3x<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 id=\"h-finalizando-polinomios\" class=\"wp-block-heading has-cyan-bluish-gray-background-color has-background\">Finalizando \u2013 Polin\u00f4mios<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Os <strong>polin\u00f4mios<\/strong> constituem uma parte fundamental da \u00e1lgebra e aparecem tanto diretamente quanto como ferramenta para diversos outros conte\u00fados matem\u00e1ticos. Por isso, compreender sua estrutura \u00e9 essencial para avan\u00e7ar em assuntos como equa\u00e7\u00f5es, fun\u00e7\u00f5es, fatora\u00e7\u00e3o, produtos not\u00e1veis e Teorema do Resto.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Nas provas, os polin\u00f4mios podem aparecer em c\u00e1lculos diretos ou inseridos em situa\u00e7\u00f5es envolvendo \u00e1reas, custos, receitas e outras rela\u00e7\u00f5es entre grandezas. Portanto, al\u00e9m de dominar as opera\u00e7\u00f5es, \u00e9 importante interpretar o enunciado e transformar as informa\u00e7\u00f5es apresentadas em express\u00f5es alg\u00e9bricas. Com uma base s\u00f3lida nesses conceitos, diversos outros temas de Matem\u00e1tica tornam-se consideravelmente mais simples. A chave para o dom\u00ednio est\u00e1 na <strong>pr\u00e1tica<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c9 importante refor\u00e7ar que este conte\u00fado <strong>deve ser utilizado como complemento ao material em PDF<\/strong>, onde a abordagem \u00e9 aprofundada e completa. Al\u00e9m disso, \u00e9 fundamental praticar com muitas quest\u00f5es, preferencialmente separadas por banca, para entender as diferentes formas de cobran\u00e7a.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Quer se aprofundar no tema? O Estrat\u00e9gia Concursos disponibiliza <strong>materiais em PDF completos e atualizados<\/strong>, com teoria detalhada, quest\u00f5es comentadas e videoaulas direcionadas para cada concurso. Com pr\u00e1tica e um bom material, voc\u00ea estar\u00e1 preparado para resolver qualquer quest\u00e3o sobre polin\u00f4mios que aparecer na sua prova.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Acesse <a href=\"https:\/\/www.estrategiaconcursos.com.br\/\" target=\"_blank\" rel=\"noreferrer noopener\">os cursos do Estrat\u00e9gia Concursos<\/a> e fortale\u00e7a sua prepara\u00e7\u00e3o com um conte\u00fado de alto n\u00edvel.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bons estudos e at\u00e9 a pr\u00f3xima!<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center\" id=\"cursos-assinatura\">Cursos e Assinaturas<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Prepare-se com o melhor material e com quem mais aprova em Concursos P\u00fablicos em todo o pa\u00eds!<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-cyan-blue-color has-text-color has-background wp-block-paragraph\" style=\"background-color:#0078bd\"><a href=\"https:\/\/concursos.estrategia.com\/portal\/concursos-abertos\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-white-color\">Concursos Abertos<\/mark><\/strong><\/a><\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-cyan-blue-color has-text-color has-background wp-block-paragraph\" style=\"background-color:#0078bd\"><a href=\"https:\/\/concursos.estrategia.com\/portal\/concursos-2026\/\" target=\"_blank\" rel=\"noreferrer noopener\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-white-color\">Concursos 2026<\/mark><\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aprenda os conceitos essenciais para resolu\u00e7\u00e3o de quest\u00f5es sobre polin\u00f4mios com um resumo para as principais provas de concursos. Ol\u00e1, pessoal! Tudo bem com voc\u00eas? As express\u00f5es alg\u00e9bricas est\u00e3o presentes em diversos conte\u00fados da Matem\u00e1tica e permitem representar rela\u00e7\u00f5es entre quantidades conhecidas e desconhecidas. Dentro desse universo, os polin\u00f4mios ocupam uma posi\u00e7\u00e3o de destaque, pois [&hellip;]<\/p>\n","protected":false},"author":3098,"featured_media":1756535,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"post_tipo":"article","footnotes":""},"categories":[2313,1,3766,220184,220242,214992,220181,1983,220182,220183,222427,1988,222278,220191,222408,220737,1984,214710,222239,222235,222236],"tags":[],"tax_estado":[219964,219965,219966,219967,219968,219969,219963,219970,219971,219972,219973,219974,219975,219976,219977,219978,219979,219980,219981,219982,219983,219984,219985,219986,219987,219988,219989,219990],"class_list":["post-1807676","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-carreiras-bancarias","category-cursos-e-concursos","category-educacional","category-engenharias-e-ti","category-estrategia-militares","category-concursos-administrativos","category-area-financeira","category-fiscal-estadual","category-fiscal-federal","category-fiscal-municipal","category-petrobras","category-policia","category-prefeituras","category-previdenciaria","category-tecnologia-da-informacao","category-tribunais-tribunais","category-tribunais","category-tribunais-de-contas","category-tribunais-regionais-federais","category-tribunal-de-justica","category-tribunal-regional-do-trabalho","tax_estado-ac","tax_estado-al","tax_estado-am","tax_estado-ap","tax_estado-ba","tax_estado-ce","tax_estado-concursos-federais","tax_estado-df","tax_estado-es","tax_estado-go","tax_estado-ma","tax_estado-mg","tax_estado-ms","tax_estado-mt","tax_estado-pa","tax_estado-pb","tax_estado-pe","tax_estado-pi","tax_estado-pr","tax_estado-rj","tax_estado-rn","tax_estado-ro","tax_estado-rr","tax_estado-rs","tax_estado-sc","tax_estado-se","tax_estado-sp","tax_estado-to"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v28.6 (Yoast SEO v28.8) - 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