Use long division to find the quotient below.

(12x3 + 3x2 - 108) = (3x-6)

O A. 4x2 + 6x + 18

O B. 4x2 + 9x + 18

O C. 4x2 - 6x + 18

D. 4x2-9x+18

B

Step-by-step explanation:

12x^3+3x^2-108 = 3x-6

3 (4x^3+x^2-36) = 3 (x-2) (divide by 3 both sides)

4x^3+x^2-36=x-2

4x^3+x^2-36

4x^3+x^2-36/x-2 =

divisor 4x^2 : (4x^2) (x-2) = 4x^3-8x^2

4x^3+x^2-36-4x^-8x^2 = 9x^2-36

then divisor is 9x : 9x (x-2) = 9x^2-18x

the remainder is : 9x^2-18x-9x^2-36 = 18x-36

then divisor is 18: 18 (x-2) = 18x-36

subtract : 18x-36 - (18x-36) = 0

the answer is 4x^2+9x+18