Factor $LaTeX: \displaystyle - 24 x^{3} - 64 x^{2} - 6 x - 16$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(12 x^{3} + 32 x^{2} + 3 x + 8)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(3 x + 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 1$ , gives $LaTeX: \displaystyle 1(3 x + 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 8$ . This gives $LaTeX: \displaystyle -2[4 x^{2} \left(3 x + 8\right) +1 \cdot \left(3 x + 8\right)] = -2\left(3 x + 8\right) \left(4 x^{2} + 1\right)$ .