Question

1 – Sejam os polinômios P(x) = x3 + 1, Q(x) = 5x2 + 2x – 1 e T(x) = x3 + x2 + x,
calcule :

a) P(x). Q(x) =
b) Q(x). T(x) =
c) T(x). P(x) =


2) Considere os polinômios: P(x) = x² – 3x + 9 e Q(x) = 2x + 3. Realize a multiplicação entre estes polinômios.

Answer 1

Resposta:

1. a) $5x^5+2x^4-x^3+5x^2+2x-1$

  b) $5x^5+7x^4+6x^3+x^2-x$

  c) $x^6+x^5+x^4+x^3+x^2+x$

2. $2x^3-3x^2+9x+27$

Explicação passo-a-passo:

1. a)  $P(x).Q(x)=\\(x^3+1).(5x^2+2x-1)=\\5x^5+2x^4-x^3+5x^2+2x-1$

  b)  $Q(x).T(x)=\\(5x^2+2x-1).(x^3+x^2+x)=\\5x^5+5x^4+5x^3+2x^4+2x^3+2x^2-x^3-x^2-x=\\5x^5+5x^4+2x^4+5x^3+2x^3-x^3+2x^2-x^2-x=\\5x^5+7x^4+7x^3-x^3+x^2-x=\\5x^5+7x^4+6x^3+x^2-x$

  c)  $T(x).P(x)=\\(x^3+x^2+x).(x^3+1)=\\x^6+x^3+x^5+x^2+x^4+x=\\x^6+x^5+x^4+x^3+x^2+x$

2.  $P(x).Q(x)=\\(x^2-3x+9).(2x+3)=\\2x^3+3x^2-6x^2-9x+18x+27=\\2x^3-3x^2+9x+27$