Find one factor of the form $a^{k}+m$, where $a^{k}$ divides the monomial with the highest power $a^{10}$ and $m$ divides the constant factor $1$. One such factor is $a^{5}-1$. Factor the polynomial by dividing it by this factor.
$$\left(a^{5}-1\right)\left(a^{5}-1\right)$$
Consider $a^{5}-1$. By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $-1$ and $q$ divides the leading coefficient $1$. One such root is $1$. Factor the polynomial by dividing it by $a-1$.
