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\frac{-x^{4}-4x^{2}+12}{4}
Factor out \frac{1}{4}.
\left(x^{2}+6\right)\left(-x^{2}+2\right)
Consider -x^{4}-4x^{2}+12. 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 12. One such factor is x^{2}+6. Factor the polynomial by dividing it by this factor.
\frac{\left(x^{2}+6\right)\left(-x^{2}+2\right)}{4}
Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -x^{2}+2,x^{2}+6.