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