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

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