Factor $LaTeX: \displaystyle - 16 x^{3} + 24 x^{2} + 24 x - 36$ .

Factoring out the GCF $LaTeX: \displaystyle -4$ from each term gives $LaTeX: \displaystyle -4(4 x^{3} - 6 x^{2} - 6 x + 9)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(2 x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(2 x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x - 3$ . This gives $LaTeX: \displaystyle -4[2 x^{2} \left(2 x - 3\right) -3 \cdot \left(2 x - 3\right)] = -4\left(2 x - 3\right) \left(2 x^{2} - 3\right)$ .