Factor 21x^2-77x-28

$21 x^{2} - 77 x - 28$

Step 1

Factor $7$ out of $21 x^{2} - 77 x - 28$ .

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

$7 (3 x^{2}) - 77 x - 28$

Factor $7$ out of $- 77 x$ .

$7 (3 x^{2}) + 7 (- 11 x) - 28$

Factor $7$ out of $- 28$ .

$7 (3 x^{2}) + 7 (- 11 x) + 7 (- 4)$

Factor $7$ out of $7 (3 x^{2}) + 7 (- 11 x)$ .

$7 (3 x^{2} - 11 x) + 7 (- 4)$

Factor $7$ out of $7 (3 x^{2} - 11 x) + 7 (- 4)$ .

$7 (3 x^{2} - 11 x - 4)$

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 $a \cdot c = 3 \cdot - 4 = - 12$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 x$ .

$7 (3 x^{2} - 11 (x) - 4)$

Rewrite $- 11$ as $1$ plus $- 12$

$7 (3 x^{2} + (1 - 12) x - 4)$

Apply the distributive property.

$7 (3 x^{2} + 1 x - 12 x - 4)$

Multiply $x$ by $1$ .

$7 (3 x^{2} + x - 12 x - 4)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$7 ((3 x^{2} + x) - 12 x - 4)$

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

$7 (x (3 x + 1) - 4 (3 x + 1))$

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$7 ((3 x + 1) (x - 4))$

Remove unnecessary parentheses.

$7 (3 x + 1) (x - 4)$

Factor 21x^2-77x-28

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