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.
答
∵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