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