Factor $LaTeX: \displaystyle 8 x^{3} + 32 x^{2} - 7 x - 28$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 8 x^{2}$ , gives $LaTeX: \displaystyle 8 x^{2}(x + 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -7$ , gives $LaTeX: \displaystyle -7(x + 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 4$ . This gives $LaTeX: \displaystyle 8 x^{2} \left(x + 4\right) -7 \cdot \left(x + 4\right) = \left(x + 4\right) \left(8 x^{2} - 7\right)$ .