Question

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

Answer 1

`2n^2+5n+2`

coefficient of the first term: `2 = 2xx1`
coefficient of the last term: `2 = 2xx1`
coefficient of the middle term (using only the factors above): `5 = 2xx2+1xx1`

`2n^2+5n+2 = (2n+1)(n+2)`

Alternative method:
Treat the given expression as a quadratic set equal to zero, with the form
`an^2+bn+c`
and use the quadratic formula
`(-b+-sqrt(b^2-4ac))/(2a)`
This will given solutions
`n=-2` and `n=-1/2`
for a factoring
`2(n+2)(n+1/2)`