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