Basic Math Examples

$2 v^{3} + 6 v^{2} - 8 v - 24$

Step 1

Factor $2$ out of $2 v^{3} + 6 v^{2} - 8 v - 24$ .

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Step 1.1

Factor $2$ out of $2 v^{3}$ .

$2 (v^{3}) + 6 v^{2} - 8 v - 24$

Step 1.2

Factor $2$ out of $6 v^{2}$ .

$2 (v^{3}) + 2 (3 v^{2}) - 8 v - 24$

Step 1.3

Factor $2$ out of $- 8 v$ .

$2 (v^{3}) + 2 (3 v^{2}) + 2 (- 4 v) - 24$

Step 1.4

Factor $2$ out of $- 24$ .

$2 v^{3} + 2 (3 v^{2}) + 2 (- 4 v) + 2 \cdot - 12$

Step 1.5

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

$2 (v^{3} + 3 v^{2}) + 2 (- 4 v) + 2 \cdot - 12$

Step 1.6

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

$2 (v^{3} + 3 v^{2} - 4 v) + 2 \cdot - 12$

Step 1.7

Factor $2$ out of $2 (v^{3} + 3 v^{2} - 4 v) + 2 \cdot - 12$ .

$2 (v^{3} + 3 v^{2} - 4 v - 12)$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$2 ((v^{3} + 3 v^{2}) - 4 v - 12)$

Step 2.2

Factor out the greatest common factor (GCF) from each group.

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $v + 3$ .

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

Step 4

Rewrite $4$ as $2^{2}$ .

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

Step 5

Factor.

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Step 5.1

Factor.

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Step 5.1.1

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

$2 ((v + 3) ((v + 2) (v - 2)))$

Step 5.1.2

Remove unnecessary parentheses.

$2 ((v + 3) (v + 2) (v - 2))$

Step 5.2

Remove unnecessary parentheses.

$2 (v + 3) (v + 2) (v - 2)$