Factor $LaTeX: \displaystyle - 15 x^{3} + 15 x^{2} + 20 x - 20$ .

Factoring out the GCF $LaTeX: \displaystyle -5$ from each term gives $LaTeX: \displaystyle -5(3 x^{3} - 3 x^{2} - 4 x + 4)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 1$ . This gives $LaTeX: \displaystyle -5[3 x^{2} \left(x - 1\right) -4 \cdot \left(x - 1\right)] = -5\left(x - 1\right) \left(3 x^{2} - 4\right)$ .