By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $4$ and $q$ divides the leading coefficient $3$. One such root is $-1$. Factor the polynomial by dividing it by $x+1$. Polynomial $3x^{2}-x+4$ is not factored since it does not have any rational roots.
