Question

A forma fatorada do polinômio x3 + 7x2 + 14x + 8 é:
(A) (x+1) . (x+2) . (x+3)
(B) (x+2) . (x+3) . (x+4)
(C) (x+1) . (x+2) . (x+4)
(D) (x+1) . (x-2) . (x+3)
(E) (x-1) . (x-4) . (x+3)

Answer 1

1+2+4=7 => (7x²)
1•2 +1•4 +2•4 = 14 => (14x)
1.2.4=8

C) (x+1) . (x+2) . (x+4) ✓

Answer 2

Olá!

$x^3 + 7x^2 +14x + 8 \\ = x^3 + 8 +7x^2 +14x \\ = x^3 + 2^3 + 7x^2 +14x \\ = (x+2) \big(x^2 -2x + 4 \big) + 7x(x + 2) \\ = (x+2) \big( x^2 -2x + 4 +7x \big) \\ = (x+2) \big( x^2 +5x + 4 \big) \\ = (x+2) \big( x^2 +x+4x + 4 \big) \\ = (x+2) \big( x( x+1)+4(x+1) \big) \\ = (x+2)(x+4)(x+1) \\ = (x+1)(x+2)(x+4)$

$\textbf{Alternativa correcta: C}$


Boa interpretação!