# How do you factor completely x^2 + 10x + 21?

Sep 23, 2016

${x}^{2} + 10 x + 21 = \left(x + 7\right) \left(x + 3\right)$

#### Explanation:

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

So we want to find a pair of factors of $21$ with sum $10$

The pair $7 , 3$ works, so we find:

${x}^{2} + 10 x + 21 = \left(x + 7\right) \left(x + 3\right)$