Factor 12x^2-4x-40

$12 x^{2} - 4 x - 40$

Step 1

Factor $4$ out of $12 x^{2} - 4 x - 40$ .

Factor $4$ out of $12 x^{2}$ .

$4 (3 x^{2}) - 4 x - 40$

Factor $4$ out of $- 4 x$ .

$4 (3 x^{2}) + 4 (- x) - 40$

Factor $4$ out of $- 40$ .

$4 (3 x^{2}) + 4 (- x) + 4 (- 10)$

Factor $4$ out of $4 (3 x^{2}) + 4 (- x)$ .

$4 (3 x^{2} - x) + 4 (- 10)$

Factor $4$ out of $4 (3 x^{2} - x) + 4 (- 10)$ .

$4 (3 x^{2} - x - 10)$

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 3 \cdot - 10 = - 30$ and whose sum is $b = - 1$ .

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

$4 (3 x^{2} - (x) - 10)$

Rewrite $- 1$ as $5$ plus $- 6$

$4 (3 x^{2} + (5 - 6) x - 10)$

Apply the distributive property.

$4 (3 x^{2} + 5 x - 6 x - 10)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$4 ((3 x^{2} + 5 x) - 6 x - 10)$

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

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

Factor the polynomial by factoring out the greatest common factor, $3 x + 5$ .

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

Remove unnecessary parentheses.

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

Factor 12x^2-4x-40

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