Factor $LaTeX: \displaystyle 45 x^{3} + 27 x^{2} + 30 x + 18$ .

Factoring out the GCF $LaTeX: \displaystyle 3$ from each term gives $LaTeX: \displaystyle 3(15 x^{3} + 9 x^{2} + 10 x + 6)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(5 x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 2$ , gives $LaTeX: \displaystyle 2(5 x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 3$ . This gives $LaTeX: \displaystyle 3[3 x^{2} \left(5 x + 3\right) +2 \cdot \left(5 x + 3\right)] = 3\left(5 x + 3\right) \left(3 x^{2} + 2\right)$ .