# How do you factor by grouping 2n^2 + 5n + 2?

$2 {n}^{2} + 5 n + 2$
$= 2 {n}^{2} + 4 n + n + 2$
$= 2 n \left(n + 2\right) + 1 \left(n + 2\right)$
$= \left(2 n + 1\right) \left(n + 2\right)$
The 'trick' is the particular separation of $5 n$ into $4 n + n$, which results in the ratio of the first to second coefficients being the same as the ratio of the third to fourth coefficients.