# How do you factor x^2+31x+30?

May 23, 2016

${x}^{2} + 31 x + 30 = \left(x + 30\right) \left(x + 1\right)$

#### Explanation:

Note that $31 = 30 + 1$ and $30 = 30 \times 1$, so we find:

$\left(x + 30\right) \left(x + 1\right) = {x}^{2} + 31 + 30$

In general, given ${x}^{2} + p x + q$, if we can find $a , b$ such that $a + b = p$ and $a b = q$, then:

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