Answer
$18x^{3}+9x^{2}+2x+1=(9x^{2}+1)(2x+1)$
Work Step by Step
$18x^{3}+9x^{2}+2x+1$
Group the first two terms together. Do the same with the last two terms:
$18x^{3}+9x^{2}+2x+1=(18x^{3}+9x^{2})+(2x+1)=...$
Take out common factor $9x^{2}$ from the first parentheses:
$...=9x^{2}(2x+1)+(2x+1)=...$
Take out common factor $(2x+1)$:
$...=(9x^{2}+1)(2x+1)$
