Factor 3x^3-24

$3 x^{3} - 24$

Step 1

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

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

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

Factor $3$ out of $- 24$ .

$3 x^{3} + 3 \cdot - 8$

Factor $3$ out of $3 x^{3} + 3 \cdot - 8$ .

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

Step 2

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

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

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 $b = 2$ .

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

Step 4

Factor.

Simplify.

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

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

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

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

Remove unnecessary parentheses.

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

Factor 3x^3-24

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