Factor $LaTeX: \displaystyle - 3 x^{3} + 24 x^{2} - 6 x + 48$ .

Factoring out the GCF $LaTeX: \displaystyle -3$ from each term gives $LaTeX: \displaystyle -3(x^{3} - 8 x^{2} + 2 x - 16)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(x - 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 2$ , gives $LaTeX: \displaystyle 2(x - 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 8$ . This gives $LaTeX: \displaystyle -3[x^{2} \left(x - 8\right) +2 \cdot \left(x - 8\right)] = -3\left(x - 8\right) \left(x^{2} + 2\right)$ .