Rewrite $a^{4}-9$ as $\left(a^{2}\right)^{2}-3^{2}$. The difference of squares can be factored using the rule: $p^{2}-q^{2}=\left(p-q\right)\left(p+q\right)$. The following polynomials are not factored since they do not have any rational roots: $a^{2}-3,a^{2}+3$.
