Consider $3x^{2}+5xy-2y^{2}+6x-2y$ as a polynomial over variable $x$.
$$3x^{2}+\left(5y+6\right)x-2y^{2}-2y$$
Find one factor of the form $kx^{m}+n$, where $kx^{m}$ divides the monomial with the highest power $3x^{2}$ and $n$ divides the constant factor $-2y^{2}-2y$. One such factor is $3x-y$. Factor the polynomial by dividing it by this factor.
