Factor $LaTeX: \displaystyle 24 x^{3} - 64 x^{2} + 15 x - 40$ .

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