Factor $LaTeX: \displaystyle 24 x^{3} - 40 x^{2} - 36 x + 60$ .

Factoring out the GCF $LaTeX: \displaystyle 4$ from each term gives $LaTeX: \displaystyle 4(6 x^{3} - 10 x^{2} - 9 x + 15)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(3 x - 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(3 x - 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x - 5$ . This gives $LaTeX: \displaystyle 4[2 x^{2} \left(3 x - 5\right) -3 \cdot \left(3 x - 5\right)] = 4\left(3 x - 5\right) \left(2 x^{2} - 3\right)$ .