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)

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):

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