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

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