Factor $LaTeX: \displaystyle 3 x^{3} - 27 x^{2} + 2 x - 18$ .

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