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

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