Factor $LaTeX: \displaystyle - 32 x^{3} - 4 x^{2} - 64 x - 8$ .

Factoring out the GCF $LaTeX: \displaystyle -4$ from each term gives $LaTeX: \displaystyle -4(8 x^{3} + x^{2} + 16 x + 2)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(8 x + 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 2$ , gives $LaTeX: \displaystyle 2(8 x + 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 8 x + 1$ . This gives $LaTeX: \displaystyle -4[x^{2} \left(8 x + 1\right) +2 \cdot \left(8 x + 1\right)] = -4\left(8 x + 1\right) \left(x^{2} + 2\right)$ .