Factor $LaTeX: \displaystyle 8 x^{3} + 4 x^{2} + 72 x + 36$ .

Factoring out the GCF $LaTeX: \displaystyle 4$ from each term gives $LaTeX: \displaystyle 4(2 x^{3} + x^{2} + 18 x + 9)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(2 x + 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 9$ , gives $LaTeX: \displaystyle 9(2 x + 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x + 1$ . This gives $LaTeX: \displaystyle 4[x^{2} \left(2 x + 1\right) +9 \cdot \left(2 x + 1\right)] = 4\left(2 x + 1\right) \left(x^{2} + 9\right)$ .