Factor $LaTeX: \displaystyle - 6 x^{3} - 8 x^{2} - 48 x - 64$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(3 x^{3} + 4 x^{2} + 24 x + 32)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(3 x + 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 8$ , gives $LaTeX: \displaystyle 8(3 x + 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 4$ . This gives $LaTeX: \displaystyle -2[x^{2} \left(3 x + 4\right) +8 \cdot \left(3 x + 4\right)] = -2\left(3 x + 4\right) \left(x^{2} + 8\right)$ .