# How do you factor #x^2 + 4?

May 18, 2015

${x}^{2} + 4$ cannot be factored using real number coefficient. Depending on your class, that may be enough of an answer.

If you really need to factor completely and are allowed to use complex numbers, you can.

$- 4 = {\left(2 i\right)}^{2}$, so we can rewrite:

${x}^{2} + 4 = {x}^{2} - \left(- 4\right) = {x}^{2} - {\left(2 i\right)}^{2}$

Now factor using the difference of squares:

${x}^{2} + 4 = \left(x + 2 i\right) \left(x - 2 i\right)$

You can check this answer by multiplying.