# How do you factor 2v^2 + 11v + 5?

May 30, 2015

$2 {v}^{2} + 11 v + 5$

$= 2 {v}^{2} + v + 10 v + 5$

$= \left(2 {v}^{2} + v\right) + \left(10 v + 5\right)$

$= v \left(2 v + 1\right) + 5 \left(2 v + 1\right)$

$= \left(v + 5\right) \left(2 v + 1\right)$

How did I know to split the middle term into $v + 10 v$?

I used a variant of the AC Method:

$A = 2$, $B = 11$, $C = 5$ are the coefficients of the quadratic.

Look for a pair of factors of $A C = 10$ whose sum is $B = 11$.

$1 \times 10 = 10$ and $1 + 10 = 11$