Factor 6x^2-5x-6

$6 x^{2} - 5 x - 6$

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 $- 5 x$ .

$6 x^{2} - 5 (x) - 6$

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 6x^2-5x-6

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