Factor $LaTeX: \displaystyle 5 x^{3} - 6 x^{2} - 10 x + 12$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(5 x - 6)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -2$ , gives $LaTeX: \displaystyle -2(5 x - 6)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x - 6$ . This gives $LaTeX: \displaystyle x^{2} \left(5 x - 6\right) -2 \cdot \left(5 x - 6\right) = \left(5 x - 6\right) \left(x^{2} - 2\right)$ .