$${ p }^{ 2 } -10xp+16 { x }^{ 2 } - { q }^{ 2 } +6xq$$
Factor
$\left(-2x+p-q\right)\left(q+p-8x\right)$
Solution Steps
Consider $p^{2}-10xp+16x^{2}-q^{2}+6xq$ as a polynomial over variable $p$.
$$p^{2}-10xp+16x^{2}-q^{2}+6xq$$
Find one factor of the form $p^{k}+m$, where $p^{k}$ divides the monomial with the highest power $p^{2}$ and $m$ divides the constant factor $16x^{2}+6qx-q^{2}$. One such factor is $-8x+p+q$. Factor the polynomial by dividing it by this factor.
