Rewrite $8+125c^{6}$ as $\left(5c^{2}\right)^{3}+2^{3}$. The sum of cubes can be factored using the rule: $a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right)$. The following polynomials are not factored since they do not have any rational roots: $5c^{2}+2,25c^{4}-10c^{2}+4$.
