Precalculus Examples

$6 a^{3} + 4 a^{2} - 16 a$

Step 1

Factor $2 a$ out of $6 a^{3} + 4 a^{2} - 16 a$ .

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Step 1.1

Factor $2 a$ out of $6 a^{3}$ .

$2 a (3 a^{2}) + 4 a^{2} - 16 a$

Step 1.2

Factor $2 a$ out of $4 a^{2}$ .

$2 a (3 a^{2}) + 2 a (2 a) - 16 a$

Step 1.3

Factor $2 a$ out of $- 16 a$ .

$2 a (3 a^{2}) + 2 a (2 a) + 2 a (- 8)$

Step 1.4

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

$2 a (3 a^{2} + 2 a) + 2 a (- 8)$

Step 1.5

Factor $2 a$ out of $2 a (3 a^{2} + 2 a) + 2 a (- 8)$ .

$2 a (3 a^{2} + 2 a - 8)$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 8 = - 24$ and whose sum is $b = 2$ .

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Step 2.1.1.1

Factor $2$ out of $2 a$ .

$2 a (3 a^{2} + 2 (a) - 8)$

Step 2.1.1.2

Rewrite $2$ as $- 4$ plus $6$

$2 a (3 a^{2} + (- 4 + 6) a - 8)$

Step 2.1.1.3

Apply the distributive property.

$2 a (3 a^{2} - 4 a + 6 a - 8)$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$2 a ((3 a^{2} - 4 a) + 6 a - 8)$

Step 2.1.2.2

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

$2 a (a (3 a - 4) + 2 (3 a - 4))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $3 a - 4$ .

$2 a ((3 a - 4) (a + 2))$

Step 2.2

Remove unnecessary parentheses.

$2 a (3 a - 4) (a + 2)$