# How do you factor 5n^2 + 19n + 12?

May 22, 2015

$5 {n}^{2} + 19 n + 12$

We are looking for factors of $5 = a \times b$
and of $12 = c \times d$
such that
$a \times c + b \times d = 19$

Fortunately that are relatively few factor possibilities
$5 = 5 \times 1$
and
$12 = \left(3 \times 4\right) \text{ or " (2xx6) " or } \left(1 \times 12\right)$

and a suitable set is easily found, giving
$\left(n + 3\right) \left(5 n + 4\right)$