Algebra Examples

$14 x^{2} + 7 x - 21$

Step 1

Factor $7$ out of $14 x^{2} + 7 x - 21$ .

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Step 1.1

Factor $7$ out of $14 x^{2}$ .

$7 (2 x^{2}) + 7 x - 21$

Step 1.2

Factor $7$ out of $7 x$ .

$7 (2 x^{2}) + 7 (x) - 21$

Step 1.3

Factor $7$ out of $- 21$ .

$7 (2 x^{2}) + 7 x + 7 \cdot - 3$

Step 1.4

Factor $7$ out of $7 (2 x^{2}) + 7 x$ .

$7 (2 x^{2} + x) + 7 \cdot - 3$

Step 1.5

Factor $7$ out of $7 (2 x^{2} + x) + 7 \cdot - 3$ .

$7 (2 x^{2} + x - 3)$

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 $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = 1$ .

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Step 2.1.1.1

Multiply by $1$ .

$7 (2 x^{2} + 1 x - 3)$

Step 2.1.1.2

Rewrite $1$ as $- 2$ plus $3$

$7 (2 x^{2} + (- 2 + 3) x - 3)$

Step 2.1.1.3

Apply the distributive property.

$7 (2 x^{2} - 2 x + 3 x - 3)$

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.

$7 ((2 x^{2} - 2 x) + 3 x - 3)$

Step 2.1.2.2

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

$7 (2 x (x - 1) + 3 (x - 1))$

Step 2.1.3

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

$7 ((x - 1) (2 x + 3))$

Step 2.2

Remove unnecessary parentheses.

$7 (x - 1) (2 x + 3)$