Factor 6g^2+5g-6

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

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 $5 g$ .

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 g (3 g - 2) + 3 (3 g - 2)$

Step 3

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

$(3 g - 2) (2 g + 3)$

Factor 6g^2+5g-6

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