因式分解(x²+3x+4)(x²+3x+5)-6

问题描述:

因式分解(x²+3x+4)(x²+3x+5)-6

设x²+3x=a
则原式=(a+4)(a+5)-6
=a²+9a+14
=(a+2)(a+7)
=(x²+3x+2)(x²+3x+7)
=(x+1)(x+2)(x²+3x+7)