Factor $LaTeX: \displaystyle 8 x^{3} - 4 x^{2} - 48 x + 24$ .

Factoring out the GCF $LaTeX: \displaystyle 4$ from each term gives $LaTeX: \displaystyle 4(2 x^{3} - x^{2} - 12 x + 6)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(2 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -6$ , gives $LaTeX: \displaystyle -6(2 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x - 1$ . This gives $LaTeX: \displaystyle 4[x^{2} \left(2 x - 1\right) -6 \cdot \left(2 x - 1\right)] = 4\left(2 x - 1\right) \left(x^{2} - 6\right)$ .