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

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(32 x^{3} - 28 x^{2} + 8 x - 7)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(8 x - 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 1$ , gives $LaTeX: \displaystyle 1(8 x - 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 8 x - 7$ . This gives $LaTeX: \displaystyle -1[4 x^{2} \left(8 x - 7\right) +1 \cdot \left(8 x - 7\right)] = -\left(8 x - 7\right) \left(4 x^{2} + 1\right)$ .