Factor $LaTeX: \displaystyle 48 x^{3} - 18 x^{2} - 32 x + 12$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(24 x^{3} - 9 x^{2} - 16 x + 6)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(8 x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(8 x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 8 x - 3$ . This gives $LaTeX: \displaystyle 2[3 x^{2} \left(8 x - 3\right) -2 \cdot \left(8 x - 3\right)] = 2\left(8 x - 3\right) \left(3 x^{2} - 2\right)$ .