Factor $LaTeX: \displaystyle - 63 x^{3} - 42 x^{2} + 63 x + 42$ .

Factoring out the GCF $LaTeX: \displaystyle -21$ from each term gives $LaTeX: \displaystyle -21(3 x^{3} + 2 x^{2} - 3 x - 2)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(3 x + 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -1$ , gives $LaTeX: \displaystyle -1(3 x + 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 2$ . This gives $LaTeX: \displaystyle -21[x^{2} \left(3 x + 2\right) -1 \cdot \left(3 x + 2\right)] = -21\left(3 x + 2\right) \left(x^{2} - 1\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle -21\left(x - 1\right) \left(x + 1\right) \left(3 x + 2\right).$