Factor $LaTeX: \displaystyle 45 x^{3} + 54 x^{2} + 20 x + 24$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 9 x^{2}$ , gives $LaTeX: \displaystyle 9 x^{2}(5 x + 6)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 4$ , gives $LaTeX: \displaystyle 4(5 x + 6)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 6$ . This gives $LaTeX: \displaystyle 9 x^{2} \left(5 x + 6\right) +4 \cdot \left(5 x + 6\right) = \left(5 x + 6\right) \left(9 x^{2} + 4\right)$ .