Precalculus Examples

$x^{4} + 1$

Step 1

Multiply the constant in the polynomial $x^{4} + 1$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

$x^{4} - 1 i^{2}$

Step 2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

${(x^{2})}^{2} - 1 i^{2}$

Step 3

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

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