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\left(x^{3}-24\right)\left(x^{3}+20\right)
Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{6} and m divides the constant factor -480. One such factor is x^{3}-24. 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}-24,x^{3}+20.