Factor $LaTeX: \displaystyle - 9 x^{3} + 18 x^{2} + 18 x - 36$ .

Factoring out the GCF $LaTeX: \displaystyle -9$ from each term gives $LaTeX: \displaystyle -9(x^{3} - 2 x^{2} - 2 x + 4)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(x - 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(x - 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 2$ . This gives $LaTeX: \displaystyle -9[x^{2} \left(x - 2\right) -2 \cdot \left(x - 2\right)] = -9\left(x - 2\right) \left(x^{2} - 2\right)$ .