Factor $LaTeX: \displaystyle 24 x^{3} - 30 x^{2} - 16 x + 20$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(12 x^{3} - 15 x^{2} - 8 x + 10)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(4 x - 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(4 x - 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x - 5$ . This gives $LaTeX: \displaystyle 2[3 x^{2} \left(4 x - 5\right) -2 \cdot \left(4 x - 5\right)] = 2\left(4 x - 5\right) \left(3 x^{2} - 2\right)$ .