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)

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

Step-by-step 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

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

i think is g(1)=-1.

hope that i can