Factor $LaTeX: \displaystyle 36 x^{3} - 27 x^{2} + 24 x - 18$ .

Factoring out the GCF $LaTeX: \displaystyle 3$ from each term gives $LaTeX: \displaystyle 3(12 x^{3} - 9 x^{2} + 8 x - 6)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(4 x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 2$ , gives $LaTeX: \displaystyle 2(4 x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x - 3$ . This gives $LaTeX: \displaystyle 3[3 x^{2} \left(4 x - 3\right) +2 \cdot \left(4 x - 3\right)] = 3\left(4 x - 3\right) \left(3 x^{2} + 2\right)$ .