By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $-5$ and $q$ divides the leading coefficient $-6$. One such root is $\frac{1}{2}$. Factor the polynomial by dividing it by $2x-1$. Polynomial $-3x^{2}-3x+5$ is not factored since it does not have any rational roots.
