By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $64$ and $q$ divides the leading coefficient $-1$. One such root is $4$. Factor the polynomial by dividing it by $P-4$. Polynomial $-P^{2}-4P-16$ is not factored since it does not have any rational roots.
