factorize(x^2-x)^2-4(x^2-x)-12

1. Factorize (x^2-x)^2-4(x^2-x)-12

Answer:
Let y be (x^2-x).
Rewrite the formula,

y^2-4y-12
= (y^2-6y) + (2y-12)
= y(y-6) + 2 (y-6)
= (y+2) (y-6)

Because y= x^2-x
Therefore,
(y+2) (y-6)
= (x^2-x+2) (x^2-x-6)
= (x^2-x+2) (x^2-3x + 2x-6)
= (x^2-x+2) (x(x-3) + 2(x-3))
= (x^2-x+2) (x+2) (x-3)
-----------------------------------------------------------------------------------------

(x^2-x)^2-4(x^2-x)-12
=2x^4-x^2-4x2+4x-12
=2x^4-5x^2+4x-1----------------------It is the answer.

2008-08-15 21:57:42 補充：
The answer is 2x^4-5x^2+4x-12 Sorry

(x2-x)2-4(x2-x)-12
=[(x2-x)-6][(x2-x)+2]
=(x2-x-6)(x2-x+2)


2008-08-16 12:52:25 補充：
漏左一步:
=(x^2-x-6)(x^2-x+2)
=(x-3)(x+2)(x^2-x+2)