Question

Completely factor 4x^3 - 12x^2 + 2x - 6

A. (4x^2 + 3)(x - 2)
B. (4x^2 + 2)(x - 3)
C. (4x^2 - 2)(x + 3)
D. (4x^2 - 3)(x + 2)

Answer 1

B. (4x^2 + 2)(x - 3)

Explanation:

4x^3 - 12x^2 + 2x - 6

Factor by grouping

4x^3 - 12x^2 + 2x - 6

Factor 4x^2 out of the first group and 2 out of the second group

4x^2 (x-3) +2(x-3)

Now factor out (x-3)

(x-3) (4x^2 +2)

To factor completely we should factor out a 2

(x-3) 2 (2x^2 +1)

2 (x-3 )(2x^2+1) but since this is not one of the choices, go with B