Consider $x^{2}-6x+8-y^{2}+2y$ as a polynomial over variable $x$.
$$x^{2}-6x+8-y^{2}+2y$$
Find one factor of the form $x^{k}+m$, where $x^{k}$ divides the monomial with the highest power $x^{2}$ and $m$ divides the constant factor $-y^{2}+2y+8$. One such factor is $x-y-2$. Factor the polynomial by dividing it by this factor.
