$${ p }^{ 4 } -8 { p }^{ 2 } -33-14q- { q }^{ 2 }$$
Factor
$\left(p^{2}-q-11\right)\left(p^{2}+q+3\right)$
Solution Steps
Consider $p^{4}-8p^{2}-33-14q-q^{2}$ as a polynomial over variable $p$.
$$p^{4}-8p^{2}-33-14q-q^{2}$$
Find one factor of the form $p^{k}+m$, where $p^{k}$ divides the monomial with the highest power $p^{4}$ and $m$ divides the constant factor $-q^{2}-14q-33$. One such factor is $p^{2}+q+3$. Factor the polynomial by dividing it by this factor.
