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\left(a^{3}-10\right)\left(a^{3}+3\right)
Find one factor of the form a^{k}+m, where a^{k} divides the monomial with the highest power a^{6} and m divides the constant factor -30. One such factor is a^{3}-10. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: a^{3}-10,a^{3}+3.