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\left(p+3\right)\left(p^{2}-3p+9\right)
Rewrite p^{3}+27 as p^{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 p^{2}-3p+9 is not factored since it does not have any rational roots.