Factor $LaTeX: \displaystyle 54 x^{3} + 27 x^{2} + 6 x + 3$ .

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