Answer:
(x - 2)(x + 1)(2x -1)
Step-by-step explanation:
We use synthetic division as a tool for factoring the given expression. The coefficients of the terms given are {2, -3, -3, 2}. If x - 2 is a factor of this expression, then 2 is a root. We perform synthetic division as follows:
2 / 2 -3 -3 2
4 2 -2
-------------------------------
2 1 -1 0
Next, we determine whether or not (2x - 1)(x + 1) represents the remaining factor(s). Using -1 as divisor, we get:
-1 / 2 1 -1
-2 1
---------------------
2 -1 0
Since the remainder is zero, x + 1 must be a factor and (2x - 1) the third factor. Answer D is correct.
