Factor $LaTeX: \displaystyle 18 x^{3} + 48 x^{2} - 21 x - 56$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 6 x^{2}$ , gives $LaTeX: \displaystyle 6 x^{2}(3 x + 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -7$ , gives $LaTeX: \displaystyle -7(3 x + 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 8$ . This gives $LaTeX: \displaystyle 6 x^{2} \left(3 x + 8\right) -7 \cdot \left(3 x + 8\right) = \left(3 x + 8\right) \left(6 x^{2} - 7\right)$ .