Factor 9x^2-6x-8

$9 x^{2} - 6 x - 8$

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 $a \cdot c = 9 \cdot - 8 = - 72$ and whose sum is $b = - 6$ .

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Factor $- 6$ out of $- 6 x$ .

$9 x^{2} - 6 (x) - 8$

Rewrite $- 6$ as $6$ plus $- 12$

$9 x^{2} + (6 - 12) x - 8$

Apply the distributive property.

$9 x^{2} + 6 x - 12 x - 8$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

$(9 x^{2} + 6 x) - 12 x - 8$

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

$3 x (3 x + 2) - 4 (3 x + 2)$

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

$(3 x + 2) (3 x - 4)$

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