Factor 3x^4-24x

$3 x^{4} - 24 x$

Step 1

Factor $3 x$ out of $3 x^{4} - 24 x$ .

Factor $3 x$ out of $3 x^{4}$ .

$3 x (x^{3}) - 24 x$

Factor $3 x$ out of $- 24 x$ .

$3 x (x^{3}) + 3 x (- 8)$

Factor $3 x$ out of $3 x (x^{3}) + 3 x (- 8)$ .

$3 x (x^{3} - 8)$

Step 2

Rewrite $8$ as $2^{3}$ .

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

Step 3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 2$ .

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

Step 4

Factor.

Simplify.

Move $2$ to the left of $x$ .

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

Raise $2$ to the power of $2$ .

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

Remove unnecessary parentheses.

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

Factor 3x^4-24x

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