Factor $LaTeX: \displaystyle 18 x^{3} + 60 x^{2} + 27 x + 90$ .

Factoring out the GCF $LaTeX: \displaystyle 3$ from each term gives $LaTeX: \displaystyle 3(6 x^{3} + 20 x^{2} + 9 x + 30)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(3 x + 10)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 3$ , gives $LaTeX: \displaystyle 3(3 x + 10)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 10$ . This gives $LaTeX: \displaystyle 3[2 x^{2} \left(3 x + 10\right) +3 \cdot \left(3 x + 10\right)] = 3\left(3 x + 10\right) \left(2 x^{2} + 3\right)$ .