Factor $LaTeX: \displaystyle - 24 x^{3} + 27 x^{2} + 32 x - 36$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(24 x^{3} - 27 x^{2} - 32 x + 36)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(8 x - 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(8 x - 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 8 x - 9$ . This gives $LaTeX: \displaystyle -1[3 x^{2} \left(8 x - 9\right) -4 \cdot \left(8 x - 9\right)] = -\left(8 x - 9\right) \left(3 x^{2} - 4\right)$ .