几道因式分解题.

题目

几道因式分解题.
1.（x²+2x-3)(x²+2x-24)+90
2.x^4 -4x³+4x²-9
3.(x-1)(x-2)(x-3)(x-4)-24
望高手指教.

答案

1.（x²+2x-3)(x²+2x-24)+90
=(x²+2x)²-27(x²+2x)+72+90
=(x²+2x)²-27(x²+2x)+162
=(x²+2x-18)(x²+2x-9)
2.x^4 -4x³+4x²-9
=(x²-2x)²-9
=(x²-2x+3)(x²-2x-3)
=(x²-2x+3)(x-3)(x+1)
3.(x-1)(x-2)(x-3)(x-4)-24
=[(x-1)(x-4)][(x-2)(x-3)]-24
=[(x²-5x)+4][(x²-5x)+6]-24
=(x²-5x)²+10(x²-5x)+24-24
=(x²-5x)(x²-5x+10)