By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $8$ and $q$ divides the leading coefficient $63$. One such root is $-\frac{2}{3}$. Factor the polynomial by dividing it by $3x+2$. Polynomial $21x^{2}-12x+4$ is not factored since it does not have any rational roots.
