Factor $LaTeX: \displaystyle 18 x^{3} + 10 x^{2} + 27 x + 15$ .

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