Factor each polynomial. \( 2 g^{3}+8 g^{6}+6 g^{2} \) \( \begin{array}{ll}\text { a. } 2 g^{1}\left(g^{2}+4 g^{5}+3 g\right) & \text { c. } 2 g^{2}\left(g+4 g^{4}+3\right) \\ \text { b. } 2 g^{2}\left(g+8 g^{6}+6 g^{2}\right) & \text { d. } 2\left(g^{3}+4 g^{6}+3 g^{2}\right)\end{array} \)

To factor the polynomial \( 2 g^{3}+8 g^{6}+6 g^{2} \), we first look for a common factor among the terms. Here, we can notice that 2 and \( g^{2} \) are common factors. Thus, we can factor out \( 2 g^{2} \): \[ 2 g^{3}+8 g^{6}+6 g^{2} = 2 g^{2}(g + 4 g^{4} + 3) \] So the correct option here is **b**. Now let's look closer at the remaining expression inside the parentheses, \( g + 4 g^{4} + 3 \). This could potentially be simplified or factored further depending on its nature, but for this polynomial, it stands as it is right now. For clarity, always remember to check if your terms can be grouped or if any identities can assist with polynomials of higher degrees! Happy factoring!