Question

2x^2+xy-y^2-4x+5y+6灵活运用所学知识，将其因式分解

Answer 1

我给你提供一个好的办法，待定系数法！聪敏的孩子！
设(2x-y+a)(x+y+b)
=2x^2+2xy+2bx-xy-y^2-by+ax+ay+ab
=2x^2+xy-y^2+(a+2b)x+(a-b)y+ab
a+2b=-4
a-b=5
3b=-9
b=-3
a=2
所以
2x^2+xy-y^2-4x+5y+6
=(2x-y+2)(x+y-3)

Answer 2

最后应该是 -6
2x^2+xy-y^2-4x+5y-6
=(2x-y)(x+y)-4x+5y-6
=(2x-y)(x+y)+(2x+2y)-6x+3y-6
=(2x-y)(x+y)+2(x+y)-6x+3y-6
=(x+y)(2x-y+2)-3(2x-y+2)
=(x+y-3)(2x-y+2）
还可以用双十字相乘法

Answer 3

应该是-6吧
2x^2+xy-y^2-4x+5y-6=(2x-y)(x+y)-4x+5y-6=(2x-y)(x+y)+(2x+2y)-6x+3y-6=(2x-y)(x+y)+2(x+y)-6x+3y-6=(x+y)(2x-y+2)-3(2x-y+2)=(x+y-3)(2x-y+2)