Factor $LaTeX: \displaystyle 18 x^{3} + 30 x^{2} - 24 x - 40$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(9 x^{3} + 15 x^{2} - 12 x - 20)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(3 x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(3 x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 5$ . This gives $LaTeX: \displaystyle 2[3 x^{2} \left(3 x + 5\right) -4 \cdot \left(3 x + 5\right)] = 2\left(3 x + 5\right) \left(3 x^{2} - 4\right)$ .