Factor 9x^2-9x-28

$9 x^{2} - 9 x - 28$

Step 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 $a \cdot c = 9 \cdot - 28 = - 252$ and whose sum is $b = - 9$ .

Factor $- 9$ out of $- 9 x$ .

$9 x^{2} - 9 (x) - 28$

Rewrite $- 9$ as $12$ plus $- 21$

$9 x^{2} + (12 - 21) x - 28$

Apply the distributive property.

$9 x^{2} + 12 x - 21 x - 28$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 x^{2} + 12 x) - 21 x - 28$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + 4$ .

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

Factor 9x^2-9x-28

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