Factor $LaTeX: \displaystyle 24 x^{3} - 12 x^{2} - 12 x + 6$ .

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