Factor $LaTeX: \displaystyle 9 x^{3} + 8 x^{2} - 81 x - 72$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(9 x + 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -9$ , gives $LaTeX: \displaystyle -9(9 x + 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 9 x + 8$ . This gives $LaTeX: \displaystyle x^{2} \left(9 x + 8\right) -9 \cdot \left(9 x + 8\right) = \left(9 x + 8\right) \left(x^{2} - 9\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle \left(x - 3\right) \left(x + 3\right) \left(9 x + 8\right).$