#### Answer

$$2x^{5}+7x^{4}-5x^{2}+7$$

#### Work Step by Step

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:
$$2x^{5}+7x^{4}-5x^{2}+7$$