{"id":61,"date":"2023-09-17T07:21:59","date_gmt":"2023-09-17T07:21:59","guid":{"rendered":"https:\/\/mathority.org\/pt\/valor-numerico-de-um-polinomio-exemplos-exercicios-resolvidos\/"},"modified":"2023-09-17T07:21:59","modified_gmt":"2023-09-17T07:21:59","slug":"valor-numerico-de-um-polinomio-exemplos-exercicios-resolvidos","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/valor-numerico-de-um-polinomio-exemplos-exercicios-resolvidos\/","title":{"rendered":"Valor num\u00e9rico de um polin\u00f4mio"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea descobrir\u00e1 o que \u00e9 e como calcular o valor num\u00e9rico de um polin\u00f4mio. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos e exerc\u00edcios resolvidos passo a passo do valor num\u00e9rico de um polin\u00f4mio. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-valor-numerico-de-un-polinomio\"><\/span> Qual \u00e9 o valor num\u00e9rico de um polin\u00f4mio?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Em matem\u00e1tica, o valor num\u00e9rico de um polin\u00f4mio P(x) para o valor x=a, ou seja P(a), \u00e9 o resultado obtido substituindo a vari\u00e1vel x do polin\u00f4mio pelo n\u00famero a e realizando os c\u00e1lculos indicados na express\u00e3o polinomial.<\/strong><\/p>\n<p> Para que voc\u00ea entenda melhor o conceito de valor num\u00e9rico de um polin\u00f4mio, mostramos a seguir como ele \u00e9 calculado com um exemplo: <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Como-calcular-el-valor-numerico-de-un-polinomo\"><\/span> Como calcular o valor num\u00e9rico de um polin\u00f4mio<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que conhecemos a defini\u00e7\u00e3o matem\u00e1tica do valor num\u00e9rico de um polin\u00f4mio, vamos ver como determinar o valor num\u00e9rico de um polin\u00f4mio usando um exemplo:<\/p>\n<ul>\n<li> Qual \u00e9 o valor num\u00e9rico do seguinte polin\u00f4mio para x=2?<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-65a7367fb9064a872fa5606d70d8327f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^3+5x^2-4x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Para encontrar o valor num\u00e9rico do polin\u00f4mio \u00e9 necess\u00e1rio avaliar o referido polin\u00f4mio no valor dado pelo problema, ou seja, \u00e9 necess\u00e1rio substituir a vari\u00e1vel<\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> do polin\u00f4mio pelo valor da instru\u00e7\u00e3o. Portanto, neste caso precisamos substituir a letra<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Para 2:<\/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-8850b99aa8c1921c96f582d9cf2d372b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=2^3+5\\cdot 2^2-4\\cdot 2+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"218\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> E assim que substituirmos o valor na express\u00e3o alg\u00e9brica do polin\u00f4mio, realizamos as opera\u00e7\u00f5es. Ent\u00e3o primeiro resolvemos para as pot\u00eancias:<\/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-9f1eb984d1fa73d02b5bed9ded3be62e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=8+5\\cdot 4-4\\cdot 2+1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"203\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Agora calculamos as multiplica\u00e7\u00f5es:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-162adaa6ea3726b7b0dd530232af86b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=8+20-8+1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> E finalmente, adicionamos e subtra\u00edmos os termos:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06e073969fc5e5b3027491d9ef7ac94b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P(2)=21}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Concluindo, o valor num\u00e9rico do polin\u00f4mio para x=2 \u00e9 igual a 21.<\/p>\n<p> Como voc\u00ea pode ver, encontrar o valor num\u00e9rico de um polin\u00f4mio n\u00e3o \u00e9 muito complicado, mas tem algumas aplica\u00e7\u00f5es muito \u00fateis. Por exemplo, saber encontrar o valor num\u00e9rico de um polin\u00f4mio \u00e9 essencial para poder usar o teorema do resto, um teorema muito importante sobre polin\u00f4mios. Clique neste link e descubra <a href=\"https:\/\/mathority.org\/pt\/exemplos-e-exercicios-do-teorema-do-resto-resolvidos\/\"><strong><span style=\"text-decoration: underline;\">o que \u00e9 o teorema do resto<\/span><\/strong><\/a> , voc\u00ea encontrar\u00e1 sua explica\u00e7\u00e3o, exemplos de uso e exerc\u00edcios resolvidos passo a passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-valores-numericos-de-polinomios\"><\/span> Exemplos de valores num\u00e9ricos de polin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para que voc\u00ea entenda como obter o valor num\u00e9rico de um polin\u00f4mio, deixamos outros exemplos resolvidos:<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 1<\/h3>\n<ul>\n<li> Calcule o valor num\u00e9rico 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-f620a315934a4ae3ceb6dfe0d8b65130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^3-2x^2+3x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<p> Para<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6de4e73609a66312d9714a253f9ae3a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-1.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\"><\/p>\n<\/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-3293713c5e12fac56d94be90f6bfc6e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(-1) &amp; =(-1)^3-2\\cdot (-1)^2+3\\cdot (-1)+6 \\\\[2ex] &amp; = -1-2\\cdot 1+3\\cdot (-1)+6 \\\\[2ex] &amp; =-1-2-3+6 \\\\[2ex]&amp;= \\bm{0} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"316\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Neste caso, o valor num\u00e9rico do polin\u00f4mio \u00e9 igual a 0. Isso tem consequ\u00eancias devido \u00e0s propriedades dos polin\u00f4mios, pois gra\u00e7as ao <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/pt\/teorema-do-fator\/\">teorema do fator<\/a><\/span><\/strong> podemos saber qual ser\u00e1 o resto de certas divis\u00f5es entre polin\u00f4mios. Para saber mais, clique no link anterior, onde explicamos o que \u00e9 e para que serve esse teorema.<\/p>\n<h3 class=\"wp-block-heading\"> Exemplo 2<\/h3>\n<ul>\n<li> Determine o valor num\u00e9rico 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-603996e6452fa70f3c1507d146c439e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=-2x^3+7x^2-8x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<p> Para<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf60bc9fcf312a246a055c15ee98033c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/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-ad8b1145d569157b4e771adfae674e2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(3) &amp; =-2\\cdot 3^3+7\\cdot 3^2-8\\cdot 3-2 \\\\[2ex] &amp; =-2\\cdot 27+7\\cdot 9-8\\cdot 3-2 \\\\[2ex] &amp; =-54+63-24-2 \\\\[2ex]&amp;= \\bm{-17} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"254\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> At\u00e9 agora vimos apenas como determinar o valor num\u00e9rico de um polin\u00f4mio da maneira cl\u00e1ssica, mas voc\u00ea deve saber que existe outro m\u00e9todo. Mais especificamente, voc\u00ea tamb\u00e9m pode calcular o valor num\u00e9rico de um polin\u00f4mio com o <a href=\"https:\/\/mathority.org\/pt\/regras-resolvidas-exemplos-exercicios-ruffini\/\"><strong><span style=\"text-decoration: underline;\">m\u00e9todo Ruffini<\/span><\/strong><\/a> . Voc\u00ea tamb\u00e9m deve saber como utilizar este procedimento, por isso recomendamos conferir sua explica\u00e7\u00e3o detalhada no link. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Valor-numerico-de-un-polinomio-con-dos-o-mas-variables\"><\/span> Valor num\u00e9rico de um polin\u00f4mio com duas ou mais vari\u00e1veis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Acabamos de ver como determinar o valor num\u00e9rico de um polin\u00f4mio quando ele possui apenas uma vari\u00e1vel. Mas\u2026 como obter o valor num\u00e9rico de um polin\u00f4mio quando ele possui mais de uma vari\u00e1vel?<\/p>\n<p> Pois bem, se um polin\u00f4mio possui 2 ou mais letras, seu valor num\u00e9rico deve ser calculado da mesma forma, <strong>ou seja, primeiro substitua cada vari\u00e1vel do polin\u00f4mio pelo seu valor correspondente e depois resolva as opera\u00e7\u00f5es polinomiais<\/strong> .<\/p>\n<p> Como exemplo, voc\u00ea tem um problema desse tipo resolvido abaixo:<\/p>\n<ul>\n<li> Encontre o valor num\u00e9rico do polin\u00f4mio multivariado\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ae6ce41951c6622a5dd702a3f74de67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y)=x^2y+4xy-2x^2+6y-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"274\" style=\"vertical-align: -5px;\"><\/p>\n<p> para os valores<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56213aa9361c3f660a6fd780c629a637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2, y=3.\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\"><\/p>\n<\/li>\n<\/ul>\n<p> Primeiro, substitu\u00edmos cada vari\u00e1vel pelo seu valor correspondente, ou seja, substitu\u00edmos a letra<\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> por 2 e mudamos a letra<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> por 3:<\/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-a0a147fbd9eac856732e746ba31bf7ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,3)=2^2\\cdot 3+4\\cdot 2\\cdot 3-2\\cdot 2^2+6\\cdot 3-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"331\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Resolvemos para as pot\u00eancias:<\/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-4e196dd787140ebfd9cf51cd22665242_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,3)=4\\cdot 3+4\\cdot 2\\cdot 3-2\\cdot 4+6\\cdot 3-5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"315\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Agora calculamos os produtos:<\/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-d086e387e69df272c991d246a5419289_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,3)=12+24-8+18-5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"234\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> E por fim fazemos as adi\u00e7\u00f5es e subtra\u00e7\u00f5es:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a56aaa1a35d10261d6a7c885d4c5c38c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P(2,3)=41}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Portanto, o valor num\u00e9rico do polin\u00f4mio para os dados da instru\u00e7\u00e3o \u00e9 equivalente a 41. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-valor-numerico-de-un-polinomio\"><\/span> Exerc\u00edcios resolvidos sobre o valor num\u00e9rico de um polin\u00f4mio<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Exerc\u00edcio 1<\/h3>\n<p> Qual \u00e9 o valor num\u00e9rico do polin\u00f4mio P(x) para x=-2? <\/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-2058e4637803a44f702503177a9a5999_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=-2x^3-4x^2+3x+8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"222\" 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 a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para encontrar o valor num\u00e9rico do polin\u00f4mio, precisamos simplesmente substituir o valor dado na declara\u00e7\u00e3o na express\u00e3o polinomial e resolver as opera\u00e7\u00f5es resultantes: <\/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-93b7cf1a6c7e930a0a70fc8302f4012d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(-2) &amp; =-2\\cdot (-2)^3-4\\cdot (-2)^2+3\\cdot (-2)+8 \\\\[2ex] &amp; =-2\\cdot (-8)-4\\cdot 4+3\\cdot (-2)+8 \\\\[2ex] &amp; =+16-16-6+8 \\\\[2ex]&amp;= \\bm{2} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"351\" 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 2<\/h3>\n<p> Calcule o valor num\u00e9rico do seguinte polin\u00f4mio com fra\u00e7\u00f5es para x=4. <\/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-51b55d638c13c2ae521dd1b268e566b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=\\cfrac{1}{2} x^2-\\cfrac{5}{4}x + 7\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"163\" 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\"> Quer o polin\u00f4mio tenha fra\u00e7\u00f5es ou n\u00e3o, o procedimento para encontrar o valor num\u00e9rico do polin\u00f4mio \u00e9 sempre o mesmo. Devemos portanto substituir a vari\u00e1vel x por 4 e resolver os c\u00e1lculos: <\/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-04fa4389b5e7c5257937ad35aed07c7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(4) &amp; =\\cfrac{1}{2} \\cdot 4^2-\\cfrac{5}{4}\\cdot 4+ 7 \\\\[2ex] &amp; =\\cfrac{1}{2} \\cdot 16-\\cfrac{5}{4}\\cdot 4+ 7\\\\[2ex] &amp; =8-5+7 \\\\[2ex]&amp;= \\bm{10} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"181\" width=\"186\" 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 3<\/h3>\n<p> Determine o valor num\u00e9rico do polin\u00f4mio para os valores x=3, y=5 e z=-2 <\/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-93ec397c7da59b30a0550f40bb0b1c06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y,z)=x^2yz+4y^2z^2-3x^2z+6xyz\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"312\" 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 a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Para determinar o valor num\u00e9rico de um polin\u00f4mio multivariado, basta substituir os valores dados no problema na express\u00e3o alg\u00e9brica e resolver as opera\u00e7\u00f5es resultantes: <\/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-29683a91c14427a8ea42c3518e59e53f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(3,5,-2) &amp; =3^2\\cdot 5\\cdot (-2)+4\\cdot 5^2\\cdot (-2)^2-3\\cdot 3^2\\cdot (-2)+6\\cdot 3\\cdot 5 \\cdot (-2) \\\\[2ex] &amp; =9\\cdot 5\\cdot (-2)+4\\cdot 25\\cdot 4-3\\cdot 9\\cdot (-2)+6\\cdot 3\\cdot 5 \\cdot (-2) \\\\[2ex] &amp; =-90+400+54-180\\\\[2ex]&amp;= \\bm{184} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"543\" 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 4<\/h3>\n<p> Dado 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-288097fb1db706c4470871749ac23d88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)= -2x^3-3x^2+5x+k\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"222\" style=\"vertical-align: -5px;\"><\/p>\n<p> calcular o valor do par\u00e2metro<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> para que <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3029b4a44964ce05fcd5497240a906ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2)=5.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" 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 a solu\u00e7\u00e3o<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Neste problema, para encontrar o valor da inc\u00f3gnita<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> precisamos resolver a equa\u00e7\u00e3o<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3029b4a44964ce05fcd5497240a906ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2)=5.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" 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-1c57342c839d903ba49d3065a69b092c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Portanto, primeiro tentamos calcular o valor de P(-2):<\/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-3b58398099c8033b93a559e2f0c87f1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(-2) &amp; =-2\\cdot (-2)^3-3\\cdot (-2)^2+5\\cdot (-2)+k \\\\[2ex] &amp; =-2\\cdot (-8)-3\\cdot 4+5\\cdot (-2)+k \\\\[2ex] &amp; =+16-12-10+k\\\\[2ex]&amp;=-6+k \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"144\" width=\"351\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Agora igualamos a express\u00e3o obtida a 5: <\/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-1c57342c839d903ba49d3065a69b092c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" 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-e8b31008f76f38998d02a91cb976653e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-6+k=5\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E finalmente, resolvemos a equa\u00e7\u00e3o resultante: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b76441987dd8c22187ed4d37c72baea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=5+6\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" 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-30a3a62912d260d4dff9a56341e1e046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{k=11}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\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 o que \u00e9 e como calcular o valor num\u00e9rico de um polin\u00f4mio. Al\u00e9m disso, voc\u00ea poder\u00e1 ver exemplos e exerc\u00edcios resolvidos passo a passo do valor num\u00e9rico de um polin\u00f4mio. Qual \u00e9 o valor num\u00e9rico de um polin\u00f4mio? Em matem\u00e1tica, o valor num\u00e9rico de um polin\u00f4mio P(x) para o valor x=a, &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/valor-numerico-de-um-polinomio-exemplos-exercicios-resolvidos\/\"> <span class=\"screen-reader-text\">Valor num\u00e9rico de um polin\u00f4mio<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[21],"tags":[],"class_list":["post-61","post","type-post","status-publish","format-standard","hentry","category-polinomios"],"yoast_head":"<!-- This site is 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