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\left(y^{3}+6\right)\left(y^{3}-2\right)
Find one factor of the form y^{k}+m, where y^{k} divides the monomial with the highest power y^{6} and m divides the constant factor -12. One such factor is y^{3}+6. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: y^{3}-2,y^{3}+6.