Factor
\left(5x+1\right)\left(25x^{2}-5x+1\right)
Evaluate
125x^{3}+1
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\left(5x+1\right)\left(25x^{2}-5x+1\right)
Rewrite 125x^{3}+1 as \left(5x\right)^{3}+1^{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 25x^{2}-5x+1 is not factored since it does not have any rational roots.
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