Factor $LaTeX: \displaystyle - 9 x^{3} + 72 x^{2} + 3 x - 24$ .

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