Question

Factor completely x3 + 6x2 − 9x − 54.

A (x + 3)(x − 3)(x + 6)
B (x + 3)(x − 3)(x − 6)
C (x2 + 9)(x + 6)
D(x2 − 9)(x + 6

Answer 1

A (x + 3)(x - 3)(x + 6)

Explanation:

f(x) = x3 + 6x2 − 9x − 54

f(3) = 3^3 + 6(3)^2 - 9(3) - 54

= 27 + 54 - - 27 - 54 = 0

So (x - 3) is a factor.

f(-3) = 3^-3 + 6(-3)^2 - 9(-3) - 54

= -27 + 54 - 27 - 54 = 0

so (x + 3) is a factor

x + 3 * (x - 3) = x^2 - 9 and if we divide f(x) by

(x^2 - 9) we get x + 6.