Precalculus (6th Edition)

$$2x^{5}+7x^{4}-5x^{2}+7$$
Initial equation: $\frac{-4x^{7}-14x^{6}+10x^{4}-14x^{2}}{-2x^{2}}$ Begin by factoring both the numerator and denominator. In this case, only the numerator factors, and is done so by taking out a GCF: $$-2x^{2}(2x^{5}+7x^{4}-5x^{2}+7)$$ Put this back over the denominator: $$\frac{-2x^{2}(2x^{5}+7x^{4}-5x^{2}+7)}{-2x^{2}}$$ Finally, remove what cancels out to get the final answer: $$2x^{5}+7x^{4}-5x^{2}+7$$