3x^3+2x^2y-19xy^2+6y^3
=(3x^3-x^2y)+(3x^2y-19xy^2+6y^3)
=x^2(3x-y)+y(3x-y)(x-6y)
=(3x-y)(x^2+xy-6y^2)
=(3x-y)(x+3y)(x-2y)