Factor 12x^2+7x-10

$12 x^{2} + 7 x - 10$

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 $a \cdot c = 12 \cdot - 10 = - 120$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$12 x^{2} + 7 (x) - 10$

Rewrite $7$ as $- 8$ plus $15$

$12 x^{2} + (- 8 + 15) x - 10$

Apply the distributive property.

$12 x^{2} - 8 x + 15 x - 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} - 8 x) + 15 x - 10$

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

$4 x (3 x - 2) + 5 (3 x - 2)$

Step 3

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

$(3 x - 2) (4 x + 5)$

Factor 12x^2+7x-10

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