Factor $LaTeX: \displaystyle - 6 x^{3} + 24 x^{2} + 2 x - 8$ .

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