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

May 27, 2015

$2 {n}^{2} + 5 n + 2$

coefficient of the first term: $2 = 2 \times 1$
coefficient of the last term: $2 = 2 \times 1$
coefficient of the middle term (using only the factors above): $5 = 2 \times 2 + 1 \times 1$

$2 {n}^{2} + 5 n + 2 = \left(2 n + 1\right) \left(n + 2\right)$

Alternative method:
Treat the given expression as a quadratic set equal to zero, with the form
$a {n}^{2} + b n + c$
$\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$n = - 2$ and $n = - \frac{1}{2}$
$2 \left(n + 2\right) \left(n + \frac{1}{2}\right)$