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\left(x^{3}-3\right)\left(x^{6}+3x^{3}+9\right)
Rewrite x^{9}-27 as \left(x^{3}\right)^{3}-3^{3}. The difference 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: x^{3}-3,x^{6}+3x^{3}+9.