Factor 5x^2+4x-12

$5 x^{2} + 4 x - 12$

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 $a \cdot c = 5 \cdot - 12 = - 60$ and whose sum is $b = 4$ .

Factor $4$ out of $4 x$ .

$5 x^{2} + 4 (x) - 12$

Rewrite $4$ as $- 6$ plus $10$

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 5x^2+4x-12

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