Factor $LaTeX: \displaystyle 20 x^{3} + 6 x^{2} - 90 x - 27$ .

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