# How do you factor completely x^2 + 16?

Jan 15, 2017

#### Answer:

No factor in $\mathbb{R}$.
$x = 4 i$ multiplicity 2 or $x = - 4 i$ multiplicity 2 in $\mathbb{C}$

#### Explanation:

In $\mathbb{R}$,

${x}^{2} + 16 = 0$

$\implies {x}^{2} = - 16$

No solution in $\mathbb{R}$ since ${x}^{2} \ge 0$ in $\mathbb{R}$.

In $\mathbb{C}$,

${x}^{2} = - 16$

$\implies x = \sqrt{- 16}$

$\implies x = \sqrt{16} \cdot \sqrt{- 1}$

$\implies x = \pm 4 i$

x = 4i multiplicity 2 or x = -4i multiplicity 2