Factor $LaTeX: \displaystyle 48 x^{3} + 16 x^{2} - 18 x - 6$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(24 x^{3} + 8 x^{2} - 9 x - 3)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 8 x^{2}$ , gives $LaTeX: \displaystyle 8 x^{2}(3 x + 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(3 x + 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 1$ . This gives $LaTeX: \displaystyle 2[8 x^{2} \left(3 x + 1\right) -3 \cdot \left(3 x + 1\right)] = 2\left(3 x + 1\right) \left(8 x^{2} - 3\right)$ .