Factor completely 2x3 + x2 - 18x - 9

A. (x2-9) (2x+1)

B. (x-3) (x+3) (2x-1)

C. (x-3) (x+3) (2x+1)

D. (2x-3) (2x+3) (x-1)

Option C is the answer

Factor the following:

2 x^3 + x^2 - 18 x - 9

Factor terms by grouping. 2 x^3 + x^2 - 18 x - 9 = (2 x^3 + x^2) + (-18 x - 9) = x^2 (2 x + 1) - 9 (2 x + 1):

x^2 (2 x + 1) - 9 (2 x + 1)

Factor 2 x + 1 from x^2 (2 x + 1) - 9 (2 x + 1):

(2 x + 1) (x^2 - 9)

x^2 - 9 = x^2 - 3^2:

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

Factor the difference of two squares. x^2 - 3^2 = (x - 3) (x + 3):

Answer: (x - 3) (x + 3) (2 x + 1) thus the Answer is C.