Calculus Examples

$6 x^{2} + 2 x - 8$

Step 1

Factor $2$ out of $6 x^{2} + 2 x - 8$ .

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Step 1.1

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

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

Step 1.2

Factor $2$ out of $2 x$ .

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

Step 1.3

Factor $2$ out of $- 8$ .

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

Step 1.4

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

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

Step 1.5

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

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

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 $a \cdot c = 3 \cdot - 4 = - 12$ and whose sum is $b = 1$ .

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Step 2.1.1.1

Multiply by $1$ .

$2 (3 x^{2} + 1 x - 4)$

Step 2.1.1.2

Rewrite $1$ as $- 3$ plus $4$

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

Step 2.1.1.3

Apply the distributive property.

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

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.

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

Step 2.1.2.2

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

$2 (3 x (x - 1) + 4 (x - 1))$

Step 2.1.3

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

$2 ((x - 1) (3 x + 4))$

Step 2.2

Remove unnecessary parentheses.

$2 (x - 1) (3 x + 4)$