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)