Factor 21x^2-91x-70

$21 x^{2} - 91 x - 70$

Step 1

Factor $7$ out of $21 x^{2} - 91 x - 70$ .

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

$7 (3 x^{2}) - 91 x - 70$

Factor $7$ out of $- 91 x$ .

$7 (3 x^{2}) + 7 (- 13 x) - 70$

Factor $7$ out of $- 70$ .

$7 (3 x^{2}) + 7 (- 13 x) + 7 (- 10)$

Factor $7$ out of $7 (3 x^{2}) + 7 (- 13 x)$ .

$7 (3 x^{2} - 13 x) + 7 (- 10)$

Factor $7$ out of $7 (3 x^{2} - 13 x) + 7 (- 10)$ .

$7 (3 x^{2} - 13 x - 10)$

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 $a \cdot c = 3 \cdot - 10 = - 30$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 x$ .

$7 (3 x^{2} - 13 (x) - 10)$

Rewrite $- 13$ as $2$ plus $- 15$

$7 (3 x^{2} + (2 - 15) x - 10)$

Apply the distributive property.

$7 (3 x^{2} + 2 x - 15 x - 10)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$7 ((3 x^{2} + 2 x) - 15 x - 10)$

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

$7 (x (3 x + 2) - 5 (3 x + 2))$

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

$7 ((3 x + 2) (x - 5))$

Remove unnecessary parentheses.

$7 (3 x + 2) (x - 5)$

Factor 21x^2-91x-70

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