Write as a Set of Linear Factors x^4+36x^2

$x^{4} + 36 x^{2}$

Step 1

Factor $x^{2}$ out of $x^{4} + 36 x^{2}$ .

Factor $x^{2}$ out of $x^{4}$ .

$x^{2} x^{2} + 36 x^{2}$

Factor $x^{2}$ out of $36 x^{2}$ .

$x^{2} x^{2} + x^{2} \cdot 36$

Factor $x^{2}$ out of $x^{2} x^{2} + x^{2} \cdot 36$ .

$x^{2} (x^{2} + 36)$

Step 2

Factor over the complex numbers.

Multiply the constant in the polynomial $x^{2} + 36$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

$x^{2} (x^{2} - 36 i^{2})$

Rewrite $36 i^{2}$ as ${(6 i)}^{2}$ .

$x^{2} (x^{2} - {(6 i)}^{2})$

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 $i = 6 i$ .

$x^{2} ((x + 6 i) (x - (6 i)))$

Factor.

Multiply $6$ by $- 1$ .

$x^{2} ((x + 6 i) (x - 6 i))$

Remove unnecessary parentheses.

$x^{2} (x + 6 i) (x - 6 i)$