3x^2+4xy+y^2-5x-3y+2=
(3x^2+4xy+y^2)-5x-3y+2=
(3x+y)(x+y)-(3x+y)-2x-2y+2=
[(3x+y)(x+y)-(3x+y)]-2(x+y-1)=
(3x+y)(x+y-1)-2(x+y-1)=
(x+y-1)(3x+y-2)