Factor $LaTeX: \displaystyle 24 x^{3} - 64 x^{2} - 6 x + 16$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(12 x^{3} - 32 x^{2} - 3 x + 8)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(3 x - 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -1$ , gives $LaTeX: \displaystyle -1(3 x - 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x - 8$ . This gives $LaTeX: \displaystyle 2[4 x^{2} \left(3 x - 8\right) -1 \cdot \left(3 x - 8\right)] = 2\left(3 x - 8\right) \left(4 x^{2} - 1\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle 2\left(2 x - 1\right) \left(2 x + 1\right) \left(3 x - 8\right).$