Factor $LaTeX: \displaystyle - 27 x^{3} - 24 x^{2} - 18 x - 16$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(27 x^{3} + 24 x^{2} + 18 x + 16)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(9 x + 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 2$ , gives $LaTeX: \displaystyle 2(9 x + 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 9 x + 8$ . This gives $LaTeX: \displaystyle -1[3 x^{2} \left(9 x + 8\right) +2 \cdot \left(9 x + 8\right)] = -\left(9 x + 8\right) \left(3 x^{2} + 2\right)$ .