By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $2$ and $q$ divides the leading coefficient $4$. One such root is $1$. Factor the polynomial by dividing it by $a-1$. Polynomial $4a^{2}-5a-2$ is not factored since it does not have any rational roots.
