Factor 6x^2-7x-10

$6 x^{2} - 7 x - 10$

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 $a \cdot c = 6 \cdot - 10 = - 60$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$6 x^{2} - 7 (x) - 10$

Rewrite $- 7$ as $5$ plus $- 12$

$6 x^{2} + (5 - 12) x - 10$

Apply the distributive property.

$6 x^{2} + 5 x - 12 x - 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 x^{2} + 5 x) - 12 x - 10$

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

$x (6 x + 5) - 2 (6 x + 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $6 x + 5$ .

$(6 x + 5) (x - 2)$

Factor 6x^2-7x-10

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