Factor 49x^2+140x-21

$49 x^{2} + 140 x - 21$

Step 1

Factor $7$ out of $49 x^{2} + 140 x - 21$ .

Factor $7$ out of $49 x^{2}$ .

$7 (7 x^{2}) + 140 x - 21$

Factor $7$ out of $140 x$ .

$7 (7 x^{2}) + 7 (20 x) - 21$

Factor $7$ out of $- 21$ .

$7 (7 x^{2}) + 7 (20 x) + 7 (- 3)$

Factor $7$ out of $7 (7 x^{2}) + 7 (20 x)$ .

$7 (7 x^{2} + 20 x) + 7 (- 3)$

Factor $7$ out of $7 (7 x^{2} + 20 x) + 7 (- 3)$ .

$7 (7 x^{2} + 20 x - 3)$

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 7 \cdot - 3 = - 21$ and whose sum is $b = 20$ .

Factor $20$ out of $20 x$ .

$7 (7 x^{2} + 20 (x) - 3)$

Rewrite $20$ as $- 1$ plus $21$

$7 (7 x^{2} + (- 1 + 21) x - 3)$

Apply the distributive property.

$7 (7 x^{2} - 1 x + 21 x - 3)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$7 ((7 x^{2} - 1 x) + 21 x - 3)$

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

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

Factor the polynomial by factoring out the greatest common factor, $7 x - 1$ .

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

Remove unnecessary parentheses.

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

Factor 49x^2+140x-21

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