# How do you factor the expression x^2 + 5x + 4?

Apr 26, 2016

${x}^{2} + 5 x + 4 = \left(x + 4\right) \left(x + 1\right)$

#### Explanation:

Find a pair of factors of $4$ with sum $5$.

The pair $4 , 1$ works.

Hence:

${x}^{2} + 5 x + 4 = \left(x + 4\right) \left(x + 1\right)$

In general note that:

$\left(x + a\right) \left(x + b\right) = {x}^{2} + \left(a + b\right) x + a b$

So if you are given a polynomial to factor in the form:

${x}^{2} + p x + q$

then you can try finding a pair of factors of $q$ with sum $p$.

If you can find $a , b$ such that $a + b = p$ and $a b = q$, then:

${x}^{2} + p x + q = \left(x + a\right) \left(x + b\right)$