Factor $LaTeX: \displaystyle 12 x^{3} - 8 x^{2} + 27 x - 18$ .

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