Question

(x-1)(x+2)(x+3)(x+4)+24因式分解

(x-1)(x+2)(x+3)(x+4)+24因式分解

Answer 1

(x-1)(x+2)(x+3)(x+4)+24
应该是这个吧：

（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)(x ²+5x+10)

Answer 2

解:原式=(x^2+x-2)(x+3)(x+4)+24
=(x^3+4x^2+x-6)(x+4)+24
=x^4+8x^3+17x^2-2x=x(x^3+8x^2+17x-2)
符号有没有抄错呀?
(x+1)(x+2)(x+3)(x+4)-24
=(x^2+5x+4)(x^2+5x+6)-24
=(x^2+5x)^2+10(x^2+5x)=(x^2+5x+10)(x^2+5x)
=x(x+5)(x^2+5x+10)