Consider $2x^{2}+3ax+x-2a^{2}-3a-1$ as a polynomial over variable $x$.
$$2x^{2}+\left(3a+1\right)x-2a^{2}-3a-1$$
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 $-2a^{2}-3a-1$. One such factor is $2x-a-1$. Factor the polynomial by dividing it by this factor.
