Consider $x^{9}+4x^{3}+5x^{2}$. Factor out $x^{2}$.
$$x^{2}\left(x^{7}+4x+5\right)$$
Consider $x^{7}+4x+5$. 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 $x+1$.
