Factor $LaTeX: \displaystyle 27 x^{3} + 21 x^{2} - 36 x - 28$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(9 x + 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(9 x + 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 9 x + 7$ . This gives $LaTeX: \displaystyle 3 x^{2} \left(9 x + 7\right) -4 \cdot \left(9 x + 7\right) = \left(9 x + 7\right) \left(3 x^{2} - 4\right)$ .