Factor $LaTeX: \displaystyle - 2 x^{3} + 2 x^{2} + 9 x - 9$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(2 x^{3} - 2 x^{2} - 9 x + 9)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -9$ , gives $LaTeX: \displaystyle -9(x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 1$ . This gives $LaTeX: \displaystyle -1[2 x^{2} \left(x - 1\right) -9 \cdot \left(x - 1\right)] = -\left(x - 1\right) \left(2 x^{2} - 9\right)$ .