Factor each polynomial. \( \begin{array}{ll}2 m^{3}-8 m^{5}-4 m^{2} & \text { c. } 2\left(m^{3}-4 m^{5}-2 m^{2}\right) \\ \begin{array}{ll}\text { a. } 2 m^{1}\left(m^{2}-4 m^{4}-2 m\right) & \text { d. } 2 m^{2}\left(m-8 m^{5}-4 m^{2}\right) \\ \text { b. } 2 m^{2}\left(m-4 m^{3}-2\right) & \end{array} \\ \text { Please select the best answer from the choices provided }\end{array} \)

To factor the polynomial \(2m^{3}-8m^{5}-4m^{2}\), we can start by finding the greatest common factor (GCF). Here, the GCF is \(2m^{1}\). Now, we factor that out: \[ 2m^{1}(m^{2}-4m^{4}-2) \] Looking closely at the expression inside the parentheses, we can rearrange it to highlight the power of \(m\): \[ 2m^{1}(m^{2} - 4m^{4} - 2) = 2m^{1}(-4m^{4} + m^{2} - 2) \] However, the form \(m^{2} - 4m^{4} - 2\) isn't the simplest unraveling. The correct choice that reflects what we factored out is: **Answer: a. \( 2 m^{1}(m^{2}-4 m^{4}-2 m) \)** And for some extra fun facts about polynomials and their factoring, consider this: Recognizing polynomials goes all the way back to ancient civilizations! The Babylonians already had methods for solving quadratic equations that would eventually lead to modern factoring techniques. It’s fascinating how these mathematical tools have evolved and remained pivotal through centuries! On the practical side, understanding how to factor polynomials is super useful not just in math class but also in real-life scenarios like engineering and computer science. For instance, optimally designing structures involves breaking down complex equations into their fundamental parts, so engineers can make crucial calculations more manageable.