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\left(8x^{3}+9\right)\left(x^{3}-3\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 8x^{6} and n divides the constant factor -27. One such factor is 8x^{3}+9. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: x^{3}-3,8x^{3}+9.