Factor $LaTeX: \displaystyle 36 x^{3} + 20 x^{2} - 27 x - 15$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(9 x + 5)$ . 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 $LaTeX: \displaystyle 4 x^{2} \left(9 x + 5\right) -3 \cdot \left(9 x + 5\right) = \left(9 x + 5\right) \left(4 x^{2} - 3\right)$ .