Factor $LaTeX: \displaystyle 3 x^{3} + 15 x^{2} + 8 x + 40$ .

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