Factor $LaTeX: \displaystyle - 72 x^{3} + 54 x^{2} + 24 x - 18$ .

Factoring out the GCF $LaTeX: \displaystyle -6$ from each term gives $LaTeX: \displaystyle -6(12 x^{3} - 9 x^{2} - 4 x + 3)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(4 x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -1$ , gives $LaTeX: \displaystyle -1(4 x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x - 3$ . This gives $LaTeX: \displaystyle -6[3 x^{2} \left(4 x - 3\right) -1 \cdot \left(4 x - 3\right)] = -6\left(4 x - 3\right) \left(3 x^{2} - 1\right)$ .