Factor
\left(2v+3\right)\left(4v^{2}-6v+9\right)
Evaluate
8v^{3}+27
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\left(2v+3\right)\left(4v^{2}-6v+9\right)
Rewrite 27+8v^{3} as \left(2v\right)^{3}+3^{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 4v^{2}-6v+9 is not factored since it does not have any rational roots.
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