Factor $LaTeX: \displaystyle 32 x^{3} + 4 x^{2} - 24 x - 3$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(8 x + 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(8 x + 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 8 x + 1$ . This gives $LaTeX: \displaystyle 4 x^{2} \left(8 x + 1\right) -3 \cdot \left(8 x + 1\right) = \left(8 x + 1\right) \left(4 x^{2} - 3\right)$ .