Factor 9z^2+6z-8

$9 z^{2} + 6 z - 8$

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

Factor $6$ out of $6 z$ .

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 z - 2$ .

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

Factor 9z^2+6z-8

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