Factor 12p^2+20p-8

$12 p^{2} + 20 p - 8$

Step 1

Factor $4$ out of $12 p^{2} + 20 p - 8$ .

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

$4 (3 p^{2}) + 20 p - 8$

Factor $4$ out of $20 p$ .

$4 (3 p^{2}) + 4 (5 p) - 8$

Factor $4$ out of $- 8$ .

$4 (3 p^{2}) + 4 (5 p) + 4 (- 2)$

Factor $4$ out of $4 (3 p^{2}) + 4 (5 p)$ .

$4 (3 p^{2} + 5 p) + 4 (- 2)$

Factor $4$ out of $4 (3 p^{2} + 5 p) + 4 (- 2)$ .

$4 (3 p^{2} + 5 p - 2)$

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 $a \cdot c = 3 \cdot - 2 = - 6$ and whose sum is $b = 5$ .

Factor $5$ out of $5 p$ .

$4 (3 p^{2} + 5 (p) - 2)$

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

$4 (3 p^{2} + (- 1 + 6) p - 2)$

Apply the distributive property.

$4 (3 p^{2} - 1 p + 6 p - 2)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$4 ((3 p^{2} - 1 p) + 6 p - 2)$

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

$4 (p (3 p - 1) + 2 (3 p - 1))$

Factor the polynomial by factoring out the greatest common factor, $3 p - 1$ .

$4 ((3 p - 1) (p + 2))$

Remove unnecessary parentheses.

$4 (3 p - 1) (p + 2)$

Factor 12p^2+20p-8

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