Factor $LaTeX: \displaystyle - 24 x^{3} + 54 x^{2} - 28 x + 63$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(24 x^{3} - 54 x^{2} + 28 x - 63)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 6 x^{2}$ , gives $LaTeX: \displaystyle 6 x^{2}(4 x - 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 7$ , gives $LaTeX: \displaystyle 7(4 x - 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x - 9$ . This gives $LaTeX: \displaystyle -1[6 x^{2} \left(4 x - 9\right) +7 \cdot \left(4 x - 9\right)] = -\left(4 x - 9\right) \left(6 x^{2} + 7\right)$ .