Precalculus Examples

$x^{2} + 25$

Step 1

Multiply the constant in the polynomial $x^{2} + 25$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

$x^{2} - 25 i^{2}$

Step 2

Rewrite $25 i^{2}$ as ${(5 i)}^{2}$ .

$x^{2} - {(5 i)}^{2}$

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 $i = 5 i$ .

$(x + 5 i) (x - (5 i))$

Step 4

Multiply $5$ by $- 1$ .

$(x + 5 i) (x - 5 i)$