x^2+2xy-8y^2+2x+14y+k能分解为两个一次因式的积,则k=
问题描述：
x^2+2xy-8y^2+2x+14y+k能分解为两个一次因式的积,则k=
答
x^2+2xy-8y^2+2x+14y+k
=(x+4y)(x-2y)+2x+14y+k
设(x+4y)(x-2y)+2x+14y+k=(x+4y+a)(x-2y+b)
(x+4y)(x-2y)+2x+14y+k=(x+4y)(x-2y)+b(x+4y)+a(x-2y)+ab
(x+4y)(x-2y)+2x+14y+k=(x+4y)(x-2y)+(b+a)x+(4b-2a)y+ab
b+a=2 4b-2a=14 ab=k
a=-1 b=3
k=-3