Factor $LaTeX: \displaystyle 40 x^{3} + 15 x^{2} + 56 x + 21$ .

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