By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $1$ and $q$ divides the leading coefficient $-125$. One such root is $\frac{1}{5}$. Factor the polynomial by dividing it by $5c-1$. Polynomial $-25c^{2}-5c-1$ is not factored since it does not have any rational roots.
