Factor $LaTeX: \displaystyle - 32 x^{3} + 8 x^{2} + 48 x - 12$ .

Factoring out the GCF $LaTeX: \displaystyle -4$ from each term gives $LaTeX: \displaystyle -4(8 x^{3} - 2 x^{2} - 12 x + 3)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(4 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(4 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x - 1$ . This gives $LaTeX: \displaystyle -4[2 x^{2} \left(4 x - 1\right) -3 \cdot \left(4 x - 1\right)] = -4\left(4 x - 1\right) \left(2 x^{2} - 3\right)$ .