The factors of 9 – (x2 – 3x – 1)2 are
-
A.
-(x – 4)(x + 1) (x – 1)(x – 2) -
B.
(x – 4)(x – 2) (x – 1)(x + 1) -
C.
-(x – 2)(x + 1) (x – 2) (x – 1) -
D.
(x – 2)(x + 2) (x – 1)(x + 1)
Correct Answer: Option A
Explanation
9 – (x2 – 3x – 1)2 = [3 – (x2 – 3x – 1)] [3 + (x2 – 3x – 1)]
= (3 – x2 + 3x + 1)(3 + x2 – 3x – 1)
= (4 + 3x – x2)(x2 – 3x + 2)
= (4 – x)(1 + x)(x – 1)(x – 2)
= -(x – 4)(x + 1) (x – 1)(x – 2)