Factor $LaTeX: \displaystyle - 50 x^{3} + 10 x^{2} - 60 x + 12$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(25 x^{3} - 5 x^{2} + 30 x - 6)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(5 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 6$ , gives $LaTeX: \displaystyle 6(5 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x - 1$ . This gives $LaTeX: \displaystyle -2[5 x^{2} \left(5 x - 1\right) +6 \cdot \left(5 x - 1\right)] = -2\left(5 x - 1\right) \left(5 x^{2} + 6\right)$ .