By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $-25$ and $q$ divides the leading coefficient $1$. One such root is $5$. Factor the polynomial by dividing it by $x-5$.
Consider $x^{3}+5x^{2}+9x+5$. By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $5$ and $q$ divides the leading coefficient $1$. One such root is $-1$. Factor the polynomial by dividing it by $x+1$.
$$\left(x+1\right)\left(x^{2}+4x+5\right)$$
Rewrite the complete factored expression. Polynomial $x^{2}+4x+5$ is not factored since it does not have any rational roots.
