# How do you factor the trinomial a^2 - 4a - 21?

Mar 30, 2016

$\left(a + 3\right) \left(a - 7\right)$

#### Explanation:

For a trinomial of this type we can factor it by looking for two numbers which multiply together to equal $- 21$ and have a sum of$- 3$

In this case: $\left(+ 3\right)$and $\left(- 7\right)$ meet tis requirement.

$\left(+ 3\right) \left(- 7\right) = - 21$

$\left(+ 3\right) + \left(- 7\right) = - 4$

Using this information I can factor ${a}^{2} - 4 a - 21$ into:

$\left(a + 3\right) \left(a - 7\right)$