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

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