Question

pra entrega hj, me ajudem por favor!!!

1. Determine os graus dos polinomios : p(x)=-7x⁴+3x³-x²+1 , q(x)=x²+7 , h(x)= 5x.

2. Dado o polinômio p(x)= -x⁴-3x³-x²+2 , calcule o p(2).

3. Considere os polinomios p(x)=x³+3x²-2x+5 , q(x)= 2x²+3x+1 e s(x)=x-1 , determine :

a)p(x) + q(x)

b)p(x)-q(x)

c)p(x) × q(x)

d)p(x)÷ s(x)
​

Answer 1

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$\bf\large\green{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}}$

$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O\ PASSO{-}A{-}PASSO\ \ \ }}$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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☺lá novamente, Ana. Vamos a mais um exercício❗ Acompanhe a resolução abaixo, feita através de algumas manipulações algébricas, e após o resultado você encontrará um link com mais informações sobre Monômios e Polinômios e outro sobre Divisão de Polinômios que talvez te ajudem com exercícios semelhantes no futuro. ✌

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1) Ⓐ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ p(x) = 7x^4 + 3x^3 - x^2 + 1}}}$

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➡ O maior monômio deste polinômio é $7x^4$ e o seu grau é 4.

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$\large\green{\boxed{\rm~~~\red{ A)}~\gray{grau}~\pink{=}~\blue{ 4 }~~~}}$ ✅

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Ⓑ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ q(x) = x^2 + 7 }}}$

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➡ O maior monômio deste polinômio é $x^2$ e o seu grau é 2.

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$\large\green{\boxed{\rm~~~\red{ B)}~\gray{grau}~\pink{=}~\blue{ 2 }~~~}}$ ✅

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Ⓒ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ h(x) = 5x^1 }}}$

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➡ O maior monômio deste polinômio é $x^1$ e o seu grau é 1.

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$\large\green{\boxed{\rm~~~\red{ C)}~\gray{grau}~\pink{=}~\blue{ 1 }~~~}}$ ✅

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2)$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ p(2) = (-2)^4 - 3 \cdot (2)^3 - (2)^2 + 2}}}$

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$\large\sf\blue{ = 16 - 24 - 4 + 2}$

$\large\sf\blue{ = -10}$

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$\large\green{\boxed{\rm~~~\red{ 2)}~\gray{p(2)}~\pink{=}~\blue{ -10 }~~~}}$ ✅

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3) Ⓐ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ x^3 + 3x^2 - 2x + 5 + 2x^2 + 3x + 1 }}}$

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$\large\sf\blue{ = x^3 + 3x^2 + 2x^2 - 2x + 3x + 5 + 1}$

$\large\sf\blue{ = x^3 + x^2 \cdot (3 + 2) + x \cdot (-2 + 3) + 6}$

$\large\sf\blue{ = x^3 + 5x^2 + x + 6}$

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$\large\green{\boxed{\rm~~~\red{ A)}~\gray{p(x) + q(x)}~\pink{=}~\blue{ x^3 + 5x^2 + x + 6 }~~~}}$ ✅

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Ⓑ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ x^3 + 3x^2 - 2x + 5 - (2x^2 + 3x + 1) }}}$

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$\sf\blue{ = x^3 + 3x^2 - 2x + 5 - 2x^2 - 3x - 1}$

$\sf\blue{ = x^3 + x^2 - 5x + 4 }$

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$\large\green{\boxed{\rm~~~\red{ B)}~\gray{p(x) - q(x)}~\pink{=}~\blue{ x^3 + x^2 - 5x + 4}~~~}}$ ✅

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Ⓒ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ (x^3 + 3x^2 - 2x + 5) \cdot (2x^2 + 3x + 1) }}}$

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$\sf\blue{ = x^3 \cdot (2x^2 + 3x + 1) + 3x^2 \cdot (2x^2 + 3x + 1) - 2x \cdot (2x^2 + 3x + 1) + 5 \cdot (2x^2 + 3x + 1)}$

$\sf\blue{ = 2x^{2 + 3} + 3x^{1 + 3} + x^3 + 6x^{2 + 2} + 9x^{1 + 2} + 3x^2 - 4x^{2 + 1} - 6x^{1 + 1} - 2x + 10x^2 + 15x + 5}$

$\sf\blue{ = 2x^5 + 3x^4 + x^3 + 6x^4 + 9x^3 + 3x^2 - 4x^3 - 6x^2 - 2x + 10x^2 + 15x + 5}$

$\sf\blue{ = 2x^5 + 9x^4 + 6x^3 + 7x^2 + 13x + 5}$

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$\large\green{\boxed{\rm~~~\red{ C)}~\gray{p(x) \cdot q(x)}~\pink{=}~\blue{  2x^5 + 9x^4 + 6x^3 + 7x^2 + 13x + 5}~~~}}$ ✅

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Ⓓ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ (x^3 + 3x^2 - 2x + 5) \div (x - 1) }}}$

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$\blue{\left[\begin{array}{rrrr|ccr}x^3&+3x^2&-2x&+5&x&-1\\&&&&&&\\\red{-(x^3}&\red{-x^2)}&&&\green{\boxed{\blue{\sf x^2}}}&&\\&&&&&&\\&4x^2&-2x&&&&\\&&&&&&\\&\red{-(4x^2}&\red{-4x)}&&&\green{\boxed{\blue{\sf +4x}}}&\\&&&&&&\\&&2x&+5&&&\\&&&&&&\\&&\red{-(2x}&\red{-2)}&&&\green{\boxed{\blue{\sf +2}}}\\&&&&&&\\&&&+7&&&\end{array}\right]}$

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$\large\green{\boxed{\rm~~~\red{ D)}~\gray{p(x) \div s(x)}~\pink{=}~\blue{ x^2 + 4x + 2~e~resto~7 }~~~}}$ ✅

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

✈ Monômios e Polinômios (https://brainly.com.br/tarefa/35827285)

✈ Divisão de Polinômios (https://brainly.com.br/tarefa/37109819)

$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

☕ $\bf\large\blue{Bons\ estudos.}$

($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}$