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\left(x^{2}+6\right)\left(x^{2}-2\right)
Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{4} and m divides the constant factor -12. One such factor is x^{2}+6. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: x^{2}-2,x^{2}+6.