Factor $LaTeX: \displaystyle 40 x^{3} + 32 x^{2} - 30 x - 24$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(20 x^{3} + 16 x^{2} - 15 x - 12)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(5 x + 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(5 x + 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 4$ . This gives $LaTeX: \displaystyle 2[4 x^{2} \left(5 x + 4\right) -3 \cdot \left(5 x + 4\right)] = 2\left(5 x + 4\right) \left(4 x^{2} - 3\right)$ .