Algebra Examples

$3 x^{5} + 9 x^{3} + 12 x$

Step 1

Factor $3 x$ out of $3 x^{5} + 9 x^{3} + 12 x$ .

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Step 1.1

Factor $3 x$ out of $3 x^{5}$ .

$3 x (x^{4}) + 9 x^{3} + 12 x$

Step 1.2

Factor $3 x$ out of $9 x^{3}$ .

$3 x (x^{4}) + 3 x (3 x^{2}) + 12 x$

Step 1.3

Factor $3 x$ out of $12 x$ .

$3 x (x^{4}) + 3 x (3 x^{2}) + 3 x (4)$

Step 1.4

Factor $3 x$ out of $3 x (x^{4}) + 3 x (3 x^{2})$ .

$3 x (x^{4} + 3 x^{2}) + 3 x (4)$

Step 1.5

Factor $3 x$ out of $3 x (x^{4} + 3 x^{2}) + 3 x (4)$ .

$3 x (x^{4} + 3 x^{2} + 4)$

Step 2

Rewrite the middle term.

$3 x (x^{4} + 2 x^{2} \cdot 2 - x^{2} + 4)$

Step 3

Rearrange terms.

$3 x (x^{4} + 2 x^{2} \cdot 2 + 4 - x^{2})$

Step 4

Factor first three terms by perfect square rule.

$3 x ({(x^{2} + 2)}^{2} - x^{2})$

Step 5

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

$3 x ((x^{2} + 2 + x) (x^{2} + 2 - x))$

Step 6

Factor.

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Step 6.1

Simplify.

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Step 6.1.1

Reorder terms.

$3 x ((x^{2} + x + 2) (x^{2} + 2 - x))$

Step 6.1.2

Reorder terms.

$3 x ((x^{2} + x + 2) (x^{2} - x + 2))$

Step 6.2

Remove unnecessary parentheses.

$3 x (x^{2} + x + 2) (x^{2} - x + 2)$