Question

(x-1)(x-2)(x-3)(x-4)-24 因式分解

要过程 可有什么公式?

Answer 1

(x-1)(x-2)(x-3)(x-4)-24
=[(x-1)(x-4)][(x-2)(x-3)]-24
=[x^2 -5x +4][x^2 -5x +6]-24
=[x^2 -5x +4][x^2 -5x +4 +2]-24
设x^2 -5x +4 为 y ，则原因式可变为
=y(y+2)-24
=y^2+2y-24
=(y+6)(y-4)
将y替换为原来的式子，那么就是
原式=(x^2 -5x +4 +6)(x^2 -5x +4 -4)
=(x^2 -5x +10)(x^2 -5x)

嗯，做好啦，用的是代元和消元的方法，看到有四次方的因式分解，肯定用到的是这个方法了，记得要多用y 来代替很复杂的x 的平方哦～～

Answer 2

(x-1)(x-2)(x-3)(x-4)-24
=[(x-1)(x-4)][(x-2)(x-3)]-24
=[(x^2-5x)+4][(x^2-5x)+6]-24
=(x^2-5x)^2+10(x^2-5x)+24-24
=(x^2-5x)^2+10(x^2-5x)
=(x^2-5x)(x^2-5x+10)
=x(x-5)(x^2-5x+10)

Answer 3

注意到1+4=2+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)
=x(x-5)(x²-5x+10)