用待定系数的方法做吧
2x^2+xy-6y^2+2x+11y-4
=(x+ay+b)(2x-6y/a-4/b)
=2x^2+(2a-6/a)xy-6y^2+(2b-4/b)x+(-6b/a-4a/b)y-4
比较系数得:2a-6/a=1……(1)
2b-4/b=2……(2)
-6b/a-4a/b=11……(3)
由(1)得:(2a+3)(a-2)=0,所以a=-3/2或2
由(2)得:(b+1)(b-2)=0,所以b=-1或2
由(3)得:(2b/a+1)(3b/a+4)=0,所以b/a=-1/2或-4/3
综上知,只有:a=2,b=-1或者a=-3/2,b=2
故2x^2+xy-6y^2+2x+11y-4=(x+2y-1)(2x-3y+4)