Factor $LaTeX: \displaystyle - 18 x^{3} + 18 x^{2} + 2 x - 2$ .

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