将x(x+1)(x-1)(x+2)-24因式分解

中间是乘号，要详细过程

2025-06-27 22:07:00

推荐回答（2个）

回答1：

x(x + 1)(x - 1)(x + 2) - 24
= x(x^2 - 1)(x + 2) - 24
= x(x^3 + 2x^2 - x - 2) - 24
= x^4 + 2x^3 - x^2 - 2x - 24
= (x^4 - 2x^3) + 4x^3 - x^2 - 2x - 24
= x^3(x - 2) + 4x^3 - 8x^2 + 7x^2 - 2x - 24
= (x^3 + 4x^2)(x - 2) + (7x^2 - 14x) + (12x - 24)
= (x^3 + 4x^2 + 7x + 12)(x - 2)
= [(x^3 + 3x^2) + (x^2 + 3x) + (4x + 12)](x - 2)
= (x^2 + x + 4)(x + 3)(x - 2)

回答2：

x(x+1)(x-1)(x+2)-24

=[x(x+1)][(x-1)(x+2)]-24

=[(x^2+x)(x^2+x-2)]-24

=(x^2+x)^2-2(x^2+x)-24

=[(x^2+x)-6][(x^2+x)+4]

=(x^2+x+4)(x+3)(x-2)