Factor $LaTeX: \displaystyle 24 x^{3} - 48 x^{2} - 40 x + 80$ .

Factoring out the GCF $LaTeX: \displaystyle 8$ from each term gives $LaTeX: \displaystyle 8(3 x^{3} - 6 x^{2} - 5 x + 10)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(x - 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -5$ , gives $LaTeX: \displaystyle -5(x - 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 2$ . This gives $LaTeX: \displaystyle 8[3 x^{2} \left(x - 2\right) -5 \cdot \left(x - 2\right)] = 8\left(x - 2\right) \left(3 x^{2} - 5\right)$ .