Factor $LaTeX: \displaystyle 24 x^{3} + 20 x^{2} - 36 x - 30$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(12 x^{3} + 10 x^{2} - 18 x - 15)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(6 x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(6 x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 6 x + 5$ . This gives $LaTeX: \displaystyle 2[2 x^{2} \left(6 x + 5\right) -3 \cdot \left(6 x + 5\right)] = 2\left(6 x + 5\right) \left(2 x^{2} - 3\right)$ .