Factor $LaTeX: \displaystyle 3 x^{3} - 9 x^{2} - 6 x + 18$ .

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