分解因式(X-1)(X-2)(X+3)(X+2)-60
问题描述：
分解因式(X-1)(X-2)(X+3)(X+2)-60
要使用换元法哦.
答
(x-1)(x-2)(x+2)(x+3)-60
=[(x-1)(x+2)][(x-2)(x+3)]-60
=[x^2+x-2][x^2+x-6]-60
=[x^2+x]^2-8[x^2+x]-48
=[x^2+x-12][x^2+x+4]
=(x+4)(x-3)(x^2+x+4)
(x-1)(x-2)(x+2)(x+3)-60
=[(x-1)(x+2)][(x-2)(x+3)]-60
=[x^2+x-2][x^2+x-6]-60
令x^2+x=a
=(a-2)(a-6)-60
=a^2-8a-48
=(a-12)(a+4)
=(x^2+x-12)(x^2+x+4)
=(x+4)(x-3)(x^2+x+4)