Factor over the Complex Numbers x^2+16

$x^{2} + 16$

Step 1

Multiply the constant in the polynomial $x^{2} + 16$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

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

Step 2

Rewrite $16 i^{2}$ as ${(4 i)}^{2}$ .

$x^{2} - {(4 i)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - i^{2} = (a + i) (a - i)$ where $a = x$ and $i = 4 i$ .

$(x + 4 i) (x - (4 i))$

Step 4

Multiply $4$ by $- 1$ .

$(x + 4 i) (x - 4 i)$