Question

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

Answer 1

`2n^2 + 5n + 2`

`= 2n^2 + 4n + n + 2`

`= 2n(n+2)+1(n+2)`

`= (2n+1)(n+2)`

The 'trick' is the particular separation of `5n` into `4n+n`, which results in the ratio of the first to second coefficients being the same as the ratio of the third to fourth coefficients.