Consider $343-x^{3}$. By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $343$ and $q$ divides the leading coefficient $-1$. One such root is $7$. Factor the polynomial by dividing it by $x-7$.
$$\left(x-7\right)\left(-x^{2}-7x-49\right)$$
Rewrite the complete factored expression. Polynomial $-x^{2}-7x-49$ is not factored since it does not have any rational roots.
