Factor each polynomial. \( -8 q^{4}+4 q^{6}-16 q^{3} \) \( \begin{array}{ll}\text { a. } 4 q^{3}\left(-2 q+q^{3}-4\right) & \text { c. } 4\left(-2 q^{4}+q^{6}-4 q^{3}\right) \\ \text { b. } 4 q^{3}\left(-2 q+4 q^{6}-16 q^{3}\right) & \text { d. } 4 q^{2}\left(-2 q^{2}+q^{4}-4 q\right)\end{array} \)

One way to factor the polynomial \( -8 q^{4}+4 q^{6}-16 q^{3} \) is by first identifying the greatest common factor (GCF). In this case, the GCF is \( -4 q^{3} \). Factoring this out gives us: \[ -8 q^{4}+4 q^{6}-16 q^{3} = -4 q^{3}(2 q^{3}-q^{2}+4) \] To find the correct factorization, we can compare it to the provided options. The correct choice would be one that accurately reflects the extraction of this GCF. Now, when looking closely, the option \( a. 4 q^{3}\left(-2 q + q^{3}-4\right) \) directly matches this factorization approach after adjusting the signs. Another method to double-check your work when factoring is to distribute back the factors you have pulled out. After you factor, always multiply the factors you found to see if they return to the original polynomial; it's a clever way to catch mistakes before declaring your answer as final! Don’t panic if your initial attempt doesn’t work—that’s simply part of the learning journey in math!