Factor $LaTeX: \displaystyle - 6 x^{3} + 30 x^{2} - 12 x + 60$ .

Factoring out the GCF $LaTeX: \displaystyle -6$ from each term gives $LaTeX: \displaystyle -6(x^{3} - 5 x^{2} + 2 x - 10)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(x - 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 2$ , gives $LaTeX: \displaystyle 2(x - 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 5$ . This gives $LaTeX: \displaystyle -6[x^{2} \left(x - 5\right) +2 \cdot \left(x - 5\right)] = -6\left(x - 5\right) \left(x^{2} + 2\right)$ .