Question

已知多项式x2x^2+3xy-2y^2-x+8y-6可分解为(x+2y+m)(2x-y+n)的形式,则m+n=? 谢=>

Answer 1

x^2+3xy-2y^2-x+8y-6
=(x+2y)(2x-y)-x+8y-6
(x+2y+m)(2x-y+n)
=(x+2y)(2x-y)+m(2x-y)+n(x+2y)+mn
=(x+2y)(2x-y)+(2m+n)x+(2n-m)y+mn
所以2m+n=-1
2n-m=8
mn=-6
m=-2,n=3
m+n=1