x^2+2xy-3y^2+3x+y+2
=(x^2+2xy-3y^2)+x+3y+2x-2y+2
=(x+3y)(x-y)+(x+3y)+2(x-y+1)
=(x+3y)(x-y+1)+2(x-y+1)
=(x+3y+2)(x-y+1)