Factor $LaTeX: \displaystyle 24 x^{3} - 16 x^{2} - 48 x + 32$ .

Factoring out the GCF $LaTeX: \displaystyle 8$ from each term gives $LaTeX: \displaystyle 8(3 x^{3} - 2 x^{2} - 6 x + 4)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(3 x - 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(3 x - 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x - 2$ . This gives $LaTeX: \displaystyle 8[x^{2} \left(3 x - 2\right) -2 \cdot \left(3 x - 2\right)] = 8\left(3 x - 2\right) \left(x^{2} - 2\right)$ .