Given that (f(x) = 2x^{3} – 3x^{2} – 11x + 6) and (f(3) = 0), factorize f(x).
-
A.
(x – 3)(x – 2)(2x + 2) -
B.
(x + 3)(x – 2)(x – 1) -
C.
(x – 3)(x + 2)(2x -1) -
D.
(x + 3)(x – 2)(2x – 1)
Correct Answer: Option C
Explanation
Since f(3) = 0, then (x – 3) is a factor of f(x).
Dividing f(x) by (x – 3), we get (2x^{2} + 3x – 2).
(2x^{2} + 3x – 2 = 2x^{2} – x + 4x – 2)
(x(2x – 1) + 2(2x – 1) = (x + 2)(2x – 1))
Therefore, (f(x) = (x – 3)(x + 2)(2x -1))