Consider $2x^{2}-3xy-2y^{2}+x+3y-1$ as a polynomial over variable $x$.
$$2x^{2}+\left(-3y+1\right)x-2y^{2}+3y-1$$
Find one factor of the form $kx^{m}+n$, where $kx^{m}$ divides the monomial with the highest power $2x^{2}$ and $n$ divides the constant factor $-2y^{2}+3y-1$. One such factor is $2x+y-1$. Factor the polynomial by dividing it by this factor.
