Calculus Examples

$12 x^{2} - 6 x - 6$

Step 1

Factor $6$ out of $12 x^{2} - 6 x - 6$ .

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Step 1.1

Factor $6$ out of $12 x^{2}$ .

$6 (2 x^{2}) - 6 x - 6$

Step 1.2

Factor $6$ out of $- 6 x$ .

$6 (2 x^{2}) + 6 (- x) - 6$

Step 1.3

Factor $6$ out of $- 6$ .

$6 (2 x^{2}) + 6 (- x) + 6 (- 1)$

Step 1.4

Factor $6$ out of $6 (2 x^{2}) + 6 (- x)$ .

$6 (2 x^{2} - x) + 6 (- 1)$

Step 1.5

Factor $6$ out of $6 (2 x^{2} - x) + 6 (- 1)$ .

$6 (2 x^{2} - x - 1)$

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 $a \cdot c = 2 \cdot - 1 = - 2$ and whose sum is $b = - 1$ .

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Step 2.1.1.1

Factor $- 1$ out of $- x$ .

$6 (2 x^{2} - (x) - 1)$

Step 2.1.1.2

Rewrite $- 1$ as $1$ plus $- 2$

$6 (2 x^{2} + (1 - 2) x - 1)$

Step 2.1.1.3

Apply the distributive property.

$6 (2 x^{2} + 1 x - 2 x - 1)$

Step 2.1.1.4

Multiply $x$ by $1$ .

$6 (2 x^{2} + x - 2 x - 1)$

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.

$6 ((2 x^{2} + x) - 2 x - 1)$

Step 2.1.2.2

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

$6 (x (2 x + 1) - (2 x + 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$6 ((2 x + 1) (x - 1))$

Step 2.2

Remove unnecessary parentheses.

$6 (2 x + 1) (x - 1)$