Algebra Examples

$f (x) = x^{4} + 49 x^{2}$

Step 1

Factor $x^{2}$ out of $x^{4} + 49 x^{2}$ .

Tap for more steps...

Step 1.1

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

$f (x) = x^{2} x^{2} + 49 x^{2}$

Step 1.2

Factor $x^{2}$ out of $49 x^{2}$ .

$f (x) = x^{2} x^{2} + x^{2} \cdot 49$

Step 1.3

Factor $x^{2}$ out of $x^{2} x^{2} + x^{2} \cdot 49$ .

$f (x) = x^{2} (x^{2} + 49)$

Step 2

Factor over the complex numbers.

Tap for more steps...

Step 2.1

Multiply the constant in the polynomial $x^{2} + 49$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

$f (x) = x^{2} (x^{2} - 49 i^{2})$

Step 2.2

Rewrite $49 i^{2}$ as ${(7 i)}^{2}$ .

$f (x) = x^{2} (x^{2} - {(7 i)}^{2})$

Step 2.3

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 $i = 7 i$ .

$f (x) = x^{2} ((x + 7 i) (x - (7 i)))$

Step 2.4

Factor.

Tap for more steps...

Step 2.4.1

Multiply $7$ by $- 1$ .

$f (x) = x^{2} ((x + 7 i) (x - 7 i))$

Step 2.4.2

Remove unnecessary parentheses.

$f (x) = x^{2} (x + 7 i) (x - 7 i)$