Factor 12x^2-x-20

$12 x^{2} - x - 20$

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 $a \cdot c = 12 \cdot - 20 = - 240$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

$12 x^{2} - (x) - 20$

Rewrite $- 1$ as $15$ plus $- 16$

$12 x^{2} + (15 - 16) x - 20$

Apply the distributive property.

$12 x^{2} + 15 x - 16 x - 20$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} + 15 x) - 16 x - 20$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 5$ .

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

Factor 12x^2-x-20

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