# How do you factor 4x^2-5?

Jun 13, 2017

It is not factorable.

#### Explanation:

In order for an expression to be factor able, there must be at least a common factor. Here, in this problem, there isn't any.

$4$ and $5$ don't have any common factors and not both terms have an $x$ term. Therefore, this expression is not factorable.

Jun 13, 2017

$4 {x}^{2} - 5 = \textcolor{red}{\left(2 x + \sqrt{5}\right) \left(2 x - \sqrt{5}\right)}$

#### Explanation:

Remember that:
$\textcolor{w h i t e}{\text{XXX}} {\textcolor{c y a n}{a}}^{2} - {\textcolor{m a \ge n t a}{b}}^{2} = \left(\textcolor{c y a n}{a} + \textcolor{m a \ge n t a}{b}\right) \left(\textcolor{c y a n}{a} - \textcolor{m a \ge n t a}{b}\right)$

$4 {x}^{2} - 5$ can be written as $\textcolor{c y a n}{{\left(2 x\right)}^{2}} - \textcolor{m a \ge n t a}{{\sqrt{5}}^{2}}$