Factor 6a^2-8a-30

$6 a^{2} - 8 a - 30$

Step 1

Factor $2$ out of $6 a^{2} - 8 a - 30$ .

Factor $2$ out of $6 a^{2}$ .

$2 (3 a^{2}) - 8 a - 30$

Factor $2$ out of $- 8 a$ .

$2 (3 a^{2}) + 2 (- 4 a) - 30$

Factor $2$ out of $- 30$ .

$2 (3 a^{2}) + 2 (- 4 a) + 2 (- 15)$

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

$2 (3 a^{2} - 4 a) + 2 (- 15)$

Factor $2$ out of $2 (3 a^{2} - 4 a) + 2 (- 15)$ .

$2 (3 a^{2} - 4 a - 15)$

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 $a \cdot c = 3 \cdot - 15 = - 45$ and whose sum is $b = - 4$ .

Factor $- 4$ out of $- 4 a$ .

$2 (3 a^{2} - 4 (a) - 15)$

Rewrite $- 4$ as $5$ plus $- 9$

$2 (3 a^{2} + (5 - 9) a - 15)$

Apply the distributive property.

$2 (3 a^{2} + 5 a - 9 a - 15)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((3 a^{2} + 5 a) - 9 a - 15)$

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

$2 (a (3 a + 5) - 3 (3 a + 5))$

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

$2 ((3 a + 5) (a - 3))$

Remove unnecessary parentheses.

$2 (3 a + 5) (a - 3)$

Factor 6a^2-8a-30

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