Question

Sendo:
P(x) = x³- 2x e Q(x) = 2^4 + 5x³ -x² + 3x - 2, Calcule: [P(x)]² - Q(x).

Answer 1

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

sabendo que
$(A-B)^2 = A^2-2AB+B^2$

agora calculando
$[P(x)]^2\to (x^3-2x)^2 = (x^3)^2 -2*x^3 *2x + (2x)^2\\\\\ [P(x)]^2\to x^{6}-4x^4+4x^2$

.............
$[P(x)]^2 - Q(x)\\\\=x^6-4x^4 +4x^2 - (2x^4-5x^3-x^2+3x-2)\\\\=x^6-4x^4 +4x^2 -2x^4+5x^3+x^2-3x+2\\\\= x^6 + (-4x^4-2x^4)+ (5x^3)+(4x^2+x^2)+(-3x) + 2\\\\=x^6-6x^4+5x^3+5x^2-3x+2$