By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $-7$ and $q$ divides the leading coefficient $1$. One such root is $1$. Factor the polynomial by dividing it by $x-1$. Polynomial $x^{2}+4x+7$ is not factored since it does not have any rational roots.
