Factor 4a^2b-14ab-30b

$4 a^{2} b - 14 a b - 30 b$

Step 1

Factor $2 b$ out of $4 a^{2} b - 14 a b - 30 b$ .

Factor $2 b$ out of $4 a^{2} b$ .

$2 b (2 a^{2}) - 14 a b - 30 b$

Factor $2 b$ out of $- 14 a b$ .

$2 b (2 a^{2}) + 2 b (- 7 a) - 30 b$

Factor $2 b$ out of $- 30 b$ .

$2 b (2 a^{2}) + 2 b (- 7 a) + 2 b (- 15)$

Factor $2 b$ out of $2 b (2 a^{2}) + 2 b (- 7 a)$ .

$2 b (2 a^{2} - 7 a) + 2 b (- 15)$

Factor $2 b$ out of $2 b (2 a^{2} - 7 a) + 2 b (- 15)$ .

$2 b (2 a^{2} - 7 a - 15)$

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 $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 a$ .

$2 b (2 a^{2} - 7 (a) - 15)$

Rewrite $- 7$ as $3$ plus $- 10$

$2 b (2 a^{2} + (3 - 10) a - 15)$

Apply the distributive property.

$2 b (2 a^{2} + 3 a - 10 a - 15)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 b ((2 a^{2} + 3 a) - 10 a - 15)$

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

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

Factor the polynomial by factoring out the greatest common factor, $2 a + 3$ .

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

Remove unnecessary parentheses.

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

Factor 4a^2b-14ab-30b

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