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

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