Factor
\left(3x^{3}+8\right)\left(9x^{6}-24x^{3}+64\right)
Evaluate
27x^{9}+512
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\left(3x^{3}+8\right)\left(9x^{6}-24x^{3}+64\right)
Rewrite 512+27x^{9} as \left(3x^{3}\right)^{3}+8^{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: 3x^{3}+8,9x^{6}-24x^{3}+64.
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