Question

4x^2+xy-y^2-4x+5y-6因式分解

Answer 1

是不是:2x^2+xy-y^2-4x+5y-6因式分解

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)

方法二:

将2x^2+xy-y^2因式分解：2x^2+xy-y^2＝(2x-y)(x+y)
那么假设2x^2+xy-y^2-4x+5y-6可以分解为(2x-y+a)(x+y+b)
展开：2x^2+xy-y^2+(a+2b)x+(a-b)y+ab
那么：a+2b=-4, a-b=5, ab=-6
解出a＝2，b＝－3
所以：2x^2+xy-y^2-4x+5y-6＝(2x-y+2)(x+y-3)