{"id":128382,"date":"2017-11-09T08:48:30","date_gmt":"2017-11-09T10:48:30","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=128382"},"modified":"2026-05-19T19:47:23","modified_gmt":"2026-05-19T21:47:23","slug":"funcao-polinomial","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/funcao-polinomial","title":{"rendered":"Fun\u00e7\u00e3o Polinomial"},"content":{"rendered":"<p><b>Fun\u00e7\u00e3o Polinomial &#8211; O que \u00e9<\/b><\/p>\n<p>Uma\u00a0<b>fun\u00e7\u00e3o polinomial<\/b>\u00a0\u00e9 uma fun\u00e7\u00e3o como uma quadr\u00e1tica, uma c\u00fabica, uma qu\u00e1rtica e assim por diante, envolvendo apenas pot\u00eancias inteiras n\u00e3o negativas de x. Podemos dar uma defini\u00e7\u00e3o geral de um polin\u00f4mio e definir seu grau.<\/p>\n<p>Se voc\u00ea j\u00e1 trabalhou com n\u00fameros e vari\u00e1veis \u200b\u200bcombinados com adi\u00e7\u00e3o, subtra\u00e7\u00e3o e multiplica\u00e7\u00e3o, provavelmente j\u00e1 se deparou com polin\u00f4mios.<\/p>\n<p>Os\u00a0<b>polin\u00f4mios<\/b>\u00a0s\u00e3o uma parte fundamental da \u00e1lgebra e nos ajudam a resolver equa\u00e7\u00f5es, representar graficamente retas e curvas e modelar situa\u00e7\u00f5es do mundo real. De equa\u00e7\u00f5es lineares simples a equa\u00e7\u00f5es complexas de grau superior, os polin\u00f4mios nos permitem encontrar valores desconhecidos.<\/p>\n<p>Al\u00e9m da \u00e1lgebra, os polin\u00f4mios tamb\u00e9m s\u00e3o amplamente utilizados em f\u00edsica e engenharia, orientando cientistas no projeto de tudo, desde foguetes a pontes.<\/p>\n<p>Uma\u00a0<strong>fun\u00e7\u00e3o polinomial<\/strong>\u00a0\u00e9 composta por mon\u00f4mios que por sua vez s\u00e3o termos do tipo\u00a0<em>a<sub>i<\/sub>x<sup>i<\/sup><\/em>\u00a0em que\u00a0<em>i<\/em>\u00a0\u00e9 um n\u00famero natural. A forma generalizada de uma fun\u00e7\u00e3o polinomial P \u00e9<\/p>\n<p class=\"imagem\">P(x) = a<sub>n<\/sub>x<sup>n<\/sup>\u00a0+ a<sub>n-1<\/sub>\u00a0x<sup>n-1<\/sup>\u00a0+ \u2026 + a<sub>2<\/sub>x<sup>2<\/sup>\u00a0+ a<sub>1<\/sub>x<sup>1<\/sup>\u00a0+ a<sub>0<\/sub><\/p>\n<p>Uma fun\u00e7\u00e3o polinomial ou polin\u00f4mio \u00e9 classificada pelo seu grau, que \u00e9 o maior expoente\u00a0da fun\u00e7\u00e3o com coeficiente n\u00e3o nulo.<\/p>\n<p><strong>Exemplo:<\/strong>\u00a0P(x) = 4x\u00b3 + 2x\u00b2 \u2013 9x \u2013 7 \u00e9 um polin\u00f4mio do terceiro grau<\/p>\n<p><strong>Exemplo:<\/strong>\u00a0P(x) = x\u2075 \u2013 1 \u00e9 um polin\u00f4mio de quinto grau<\/p>\n<p><strong>Propriedades das Fun\u00e7\u00f5es Polinomiais<\/strong><\/p>\n<p>A soma de dois polin\u00f4mios sempre gera um polin\u00f4mio<\/p>\n<p>A multiplica\u00e7\u00e3o entre dois polin\u00f4mios sempre gera um polin\u00f4mio<\/p>\n<p>O grau de uma fun\u00e7\u00e3o polinomial resultante da multiplica\u00e7\u00e3o dos polin\u00f4mios f(x) por\u00a0g(x) \u00e9 a soma dos graus de f(x) e g(x)<\/p>\n<p><strong>a)<\/strong>\u00a0<b>Exemplo:<\/b>\u00a0f(x) = x\u2074 + 2 , g(x) = x\u00b2 \u2013 3x . O grau do polin\u00f4mio resultante da\u00a0multiplica\u00e7\u00e3o entre f(x) e g(x) \u00e9 6. Fa\u00e7a a multiplica\u00e7\u00e3o e confira.<\/p>\n<p>O grau de uma fun\u00e7\u00e3o polinomial resultante da soma dos polin\u00f4mios f(x) e g(x) \u00e9 o\u00a0maior grau entre f(x) e g(x)<\/p>\n<p><strong>a)<\/strong>\u00a0<b>Exemplo:<\/b>\u00a0f(x) = x\u2077 + 2x\u00b2, g(x) = 7x\u2074 + 2x. A soma possui grau 7.<\/p>\n<p><strong>Polin\u00f4mios Not\u00e1veis<\/strong><\/p>\n<p><strong>Polin\u00f4mio de grau zero:<\/strong>\u00a0constante<\/p>\n<p><strong>a)<\/strong>\u00a0Um polin\u00f4mio de grau zero \u00e9 do tipo f(x) = k tal que k \u00e9 uma constante Real<\/p>\n<p><strong>Exemplo:<\/strong>\u00a0f(x) = 3<\/p>\n<p class=\"imagem\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-128389 size-full\" title=\"Fun\u00e7\u00e3o Constante\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-1.png\" alt=\"Fun\u00e7\u00e3o Constante\" width=\"445\" height=\"342\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-1.png 445w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-1-300x231.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><\/p>\n<p>&#8211; <strong>Polin\u00f4mio de grau um:<\/strong> fun\u00e7\u00e3o linear<\/p>\n<p>&#8211; A fun\u00e7\u00e3o linear \u00e9 bijetora e \u00e9 escrita de forma generalizada como f(x) = ax + b<\/p>\n<p><strong>Exemplo:<\/strong> fun\u00e7\u00e3o identidade f(x) = x<\/p>\n<p class=\"imagem\"><img decoding=\"async\" class=\"alignnone wp-image-128390 size-full\" title=\"Fun\u00e7\u00e3o Linear\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-2.png\" alt=\"Fun\u00e7\u00e3o Linear\" width=\"426\" height=\"323\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-2.png 426w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-2-300x227.png 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\n<p><strong>Exemplo:<\/strong> fun\u00e7\u00e3o crescente f(x) = 80x<\/p>\n<p class=\"imagem\"><img decoding=\"async\" class=\"alignnone wp-image-128391 size-full\" title=\"Fun\u00e7\u00e3o Crescente\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-3.png\" alt=\"Fun\u00e7\u00e3o Crescente\" width=\"430\" height=\"308\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-3.png 430w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-3-300x215.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/p>\n<p><strong>Exemplo:<\/strong> fun\u00e7\u00e3o decrescente f(x) = -45x<\/p>\n<p class=\"imagem\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-128392 size-full\" title=\"Fun\u00e7\u00e3o Decrescente\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-4.png\" alt=\"Fun\u00e7\u00e3o Decrescente\" width=\"396\" height=\"281\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-4.png 396w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-4-300x213.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/p>\n<p><strong>&#8211; Polin\u00f4mio de grau dois:<\/strong> fun\u00e7\u00e3o quadr\u00e1tica<\/p>\n<p><strong>a)<\/strong> Par\u00e1bola de concavidade para cima: f(x) = x\u00b2<\/p>\n<p class=\"imagem\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-128393 size-full\" title=\"Fun\u00e7\u00e3o Quadr\u00e1tica - Par\u00e1bola com concavidade para cima\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-5.png\" alt=\"Fun\u00e7\u00e3o Quadr\u00e1tica - Par\u00e1bola com concavidade para cima\" width=\"391\" height=\"288\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-5.png 391w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-5-300x221.png 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><\/p>\n<p><strong>b)<\/strong> Par\u00e1bola de concavidade para baixo: f(x) =<\/p>\n<p class=\"imagem\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-128394 size-full\" title=\"Fun\u00e7\u00e3o Quadr\u00e1tica - Par\u00e1bola com concavidade para baixo\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-6.png\" alt=\"Fun\u00e7\u00e3o Quadr\u00e1tica - Par\u00e1bola com concavidade para baixo\" width=\"380\" height=\"275\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-6.png 380w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/funcao-polinomial-6-300x217.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p><strong>Fonte:<\/strong>\u00a0Col\u00e9gio S\u00e3o Francisco\/Luisa Boccardo Burini\/www.mathcentre.ac.uk\/www.mathnasium.com<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fun\u00e7\u00e3o Polinomial &#8211; O que \u00e9 Uma\u00a0fun\u00e7\u00e3o polinomial\u00a0\u00e9 uma fun\u00e7\u00e3o como uma quadr\u00e1tica, uma c\u00fabica, uma qu\u00e1rtica e assim por diante, envolvendo apenas pot\u00eancias inteiras n\u00e3o negativas de x. Podemos dar uma defini\u00e7\u00e3o geral de um polin\u00f4mio e definir seu grau. Se voc\u00ea j\u00e1 trabalhou com n\u00fameros e vari\u00e1veis \u200b\u200bcombinados com adi\u00e7\u00e3o, subtra\u00e7\u00e3o e multiplica\u00e7\u00e3o, [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":141477,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-128382","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Fun\u00e7\u00e3o Polinomial, Polin\u00f4mios, Matem\u00e1tica Fun\u00e7\u00e3o Polinomial<\/title>\n<meta name=\"description\" content=\"Fun\u00e7\u00e3o Polinomial, Polin\u00f4mios, Matem\u00e1tica, Propriedades, \u00c1lgebra, Quadr\u00e1tica, Not\u00e1veis, Soma, Exemplo, Fun\u00e7\u00e3o Polinomial\" \/>\n<meta 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