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\left(x^{2}-2\right)\left(-x^{2}-1\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -x^{4} and n divides the constant factor 2. One such factor is x^{2}-2. 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}-1.