分解因式:(x的平方加x加1)(x的平方加x加2)减12
问题描述:
分解因式:(x的平方加x加1)(x的平方加x加2)减12
答
设y=x²+x+1
(x²+x+1)(x²+x+2)-12
=y(y+1)-12
=y²+y-12
=(y-3)(y+4)
=(x²+x+1-3)(x²+x+1+4)
=(x²+x-2)(x²+x+5)
=(x-1)(x+2)(x²+x+5)