Factor $LaTeX: \displaystyle 15 x^{3} + 24 x^{2} - 20 x - 32$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(5 x + 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(5 x + 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 8$ . This gives $LaTeX: \displaystyle 3 x^{2} \left(5 x + 8\right) -4 \cdot \left(5 x + 8\right) = \left(5 x + 8\right) \left(3 x^{2} - 4\right)$ .