Factor $LaTeX: \displaystyle 15 x^{3} - 35 x^{2} + 24 x - 56$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(3 x - 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 8$ , gives $LaTeX: \displaystyle 8(3 x - 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x - 7$ . This gives $LaTeX: \displaystyle 5 x^{2} \left(3 x - 7\right) +8 \cdot \left(3 x - 7\right) = \left(3 x - 7\right) \left(5 x^{2} + 8\right)$ .