设另一个因式为x+by-3
(x+y-2)(x+by-3)
=x^2+bxy-3x+xy+by^2-3y-2x-2by+6
=x^2+(b+1)xy+by^2-5x-(3+2b)y+6
所以b+1=a,3+2b=1
得a=0,b=-1
a+b=-1