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

Factoring out the GCF $LaTeX: \displaystyle -6$ from each term gives $LaTeX: \displaystyle -6(x^{3} - 10 x^{2} - x + 10)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(x - 10)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -1$ , gives $LaTeX: \displaystyle -1(x - 10)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 10$ . This gives $LaTeX: \displaystyle -6[x^{2} \left(x - 10\right) -1 \cdot \left(x - 10\right)] = -6\left(x - 10\right) \left(x^{2} - 1\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle -6\left(x - 10\right) \left(x - 1\right) \left(x + 1\right).$