已知多项式2x2+xy-3y2-x-4y-1=(2x+3y+m)(x-y+n),求m、n的值.

问题描述:

已知多项式2x2+xy-3y2-x-4y-1=(2x+3y+m)(x-y+n),求m、n的值.

∵2x2+xy-3y2-x-4y-1=(2x+3y+m)(x-y+n),
∴2x2+xy-3y2-x-4y-1
=(2x+3y+m)(x-y+n)
=2x2-2xy+2xn+3xy-3y2+3yn+mx-my+mn,
=2x2+xy-3y2+(3n-m)y+(m+2n)x+mn,

m+2n=−1
3n−m=−4
mn=−1

解得:
m=1
n=−1