Question

Por favor peço que me ajudem estou desesperada com esta questão de exatas
MULTIPLICAÇÃO DE POLINÔMIOS 1 .Sendo P(X) =x2+ 2x e Q(X) = 2x^2+ x
a) P(X) . Q(X)
2. Sendo P(X) = 2x2+ x e Q(X) = x2
b) P(X) . Q(X)
3. Sendo P(X) = 2x3+ x2+ e Q(X) = x3+ 2x2
c) P(X) . Q(X)
4 .Sendo P(X) = 2x4- 3x3+ 2x2+ 6x + 1 e Q(X) = 3x4
d) P(X) . Q(X)
5. Sendo P(X) = 2x5+ 1 e Q(X) = x5

e) P(X) . Q(X)

Answer 1

Para multiplicar polinômios, faça a distributiva, multiplicando os coeficientes e some os expoentes das letras iguais

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$\underbrace{Veja:}$

1) P(x) = x² + 2x e Q(x) = 2x² + x

a) P(x) . Q(x)

$\Rightarrow~~\sf(x^2 + 2x)\cdot(2x^2 + x)$

$\footnotesize{\Rightarrow~~\sf(x^2).(2x^2)+(x^2).(x)+(2x).(2x^2)+(2x).(x)}$

$\Rightarrow~~\sf2x^4 + x^3 + 4x^3 + 2x^2$

$\therefore~~\boxed{\sf2x^4 + 5x^3 + 2x^2}$

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2) P(x) = 2x² + x e Q(x) = x²

b) P(x) . Q(x)

$\Rightarrow~~\sf(2x^2 + x)\cdot(x^2)$

$\Rightarrow~~\sf(2x^2).(x^2)+(x).(x^2)$

$\therefore~~\boxed{\sf2x^4+x^3}$

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3) P(x) = 2x³ + x² e Q(x) = x³ + 2x²

c) P(x) . Q(x)

$\Rightarrow~~\sf(2x^3 + x^2)\cdot(x^3+2x^2)$

$\footnotesize{\Rightarrow~~\sf(2x^3).(x^3)+(2x^3).(2x^2)+(x^2).(x^3)+(x^2).(2x^2)}$

$\Rightarrow~~\sf2x^6+4x^5+x^5+2x^4$

$\therefore~~\boxed{\sf2x^6+5x^5+2x^4}$

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4) P(x) = 2x⁴- 3x³+ 2x²+ 6x + 1 e Q(x) = 3x⁴

d) P(x) . Q(x)

$\Rightarrow~~\sf(2x^4-3x^3 +2x^2+6x+1)\cdot(3x^4)$

$\scriptsize{\Rightarrow~~\sf(2x^4).(3x^4)+(-3x^3).(3x^4)+(2x^2).(3x^4)+(6x).(3x^4)+(1).(3x^4)}$

$\therefore~~\boxed{\sf6x^8-9x^7+6x^6+18x^5+3x^4}$

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5) P(x) = 2x⁵ + 1 e Q(x) = x⁵

e) P(x) . Q(x)

$\Rightarrow~~\sf(2x^5+1)\cdot(x^5)$

$\Rightarrow~~\sf(2x^5).(x^5)+(1).(x^5)$

$\therefore~~\boxed{\sf2x^{10}+x^5}$