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\left(s+5\right)\left(s^{2}-5s+25\right)
Rewrite s^{3}+125 as s^{3}+5^{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). Polynomial s^{2}-5s+25 is not factored since it does not have any rational roots.