Factor 12x^2+40x-32

$12 x^{2} + 40 x - 32$

Step 1

Factor $4$ out of $12 x^{2} + 40 x - 32$ .

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

$4 (3 x^{2}) + 40 x - 32$

Factor $4$ out of $40 x$ .

$4 (3 x^{2}) + 4 (10 x) - 32$

Factor $4$ out of $- 32$ .

$4 (3 x^{2}) + 4 (10 x) + 4 (- 8)$

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

$4 (3 x^{2} + 10 x) + 4 (- 8)$

Factor $4$ out of $4 (3 x^{2} + 10 x) + 4 (- 8)$ .

$4 (3 x^{2} + 10 x - 8)$

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 $a \cdot c = 3 \cdot - 8 = - 24$ and whose sum is $b = 10$ .

Factor $10$ out of $10 x$ .

$4 (3 x^{2} + 10 (x) - 8)$

Rewrite $10$ as $- 2$ plus $12$

$4 (3 x^{2} + (- 2 + 12) x - 8)$

Apply the distributive property.

$4 (3 x^{2} - 2 x + 12 x - 8)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$4 ((3 x^{2} - 2 x) + 12 x - 8)$

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

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

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

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

Remove unnecessary parentheses.

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

Factor 12x^2+40x-32

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