Factor 6z^2+5z-6

$6 z^{2} + 5 z - 6$

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 $a \cdot c = 6 \cdot - 6 = - 36$ and whose sum is $b = 5$ .

Factor $5$ out of $5 z$ .

$6 z^{2} + 5 (z) - 6$

Rewrite $5$ as $- 4$ plus $9$

$6 z^{2} + (- 4 + 9) z - 6$

Apply the distributive property.

$6 z^{2} - 4 z + 9 z - 6$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 z^{2} - 4 z) + 9 z - 6$

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

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

Step 3

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

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

Factor 6z^2+5z-6

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