Factor $LaTeX: \displaystyle 40 x^{3} - 25 x^{2} - 48 x + 30$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(8 x - 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -6$ , gives $LaTeX: \displaystyle -6(8 x - 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 8 x - 5$ . This gives $LaTeX: \displaystyle 5 x^{2} \left(8 x - 5\right) -6 \cdot \left(8 x - 5\right) = \left(8 x - 5\right) \left(5 x^{2} - 6\right)$ .