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\left(c^{2}-6\right)\left(c^{2}-2\right)
Find one factor of the form c^{k}+m, where c^{k} divides the monomial with the highest power c^{4} and m divides the constant factor 12. One such factor is c^{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: c^{2}-6,c^{2}-2.