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x^{12}-2x^{7}-x^{7}-x^{5}
Combine -x^{7} and -x^{7} to get -2x^{7}.
x^{12}-3x^{7}-x^{5}
Combine -2x^{7} and -x^{7} to get -3x^{7}.
x^{5}\left(x^{7}-x^{2}-x^{2}-x^{2}-1\right)
Factor out x^{5}. Polynomial x^{7}-3x^{2}-1 is not factored since it does not have any rational roots.