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