Factor by Grouping 3x^3+24

$3 x^{3} + 24$

Factor out the GCF of $3$ from $3 x^{3} + 24$ .

Factor out the GCF of $3$ from each term in the polynomial.

Factor out the GCF of $3$ from the expression $3 x^{3}$ .

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

Factor out the GCF of $3$ from the expression $24$ .

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

Since all the terms share a common factor of $3$ , it can be factored out of each term.

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

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

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

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

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

Simplify.

Multiply $2$ by $- 1$ .

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

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

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

Factor by Grouping 3x^3+24

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