Factor 15x^2-35x-30

$15 x^{2} - 35 x - 30$

Step 1

Factor $5$ out of $15 x^{2} - 35 x - 30$ .

Factor $5$ out of $15 x^{2}$ .

$5 (3 x^{2}) - 35 x - 30$

Factor $5$ out of $- 35 x$ .

$5 (3 x^{2}) + 5 (- 7 x) - 30$

Factor $5$ out of $- 30$ .

$5 (3 x^{2}) + 5 (- 7 x) + 5 (- 6)$

Factor $5$ out of $5 (3 x^{2}) + 5 (- 7 x)$ .

$5 (3 x^{2} - 7 x) + 5 (- 6)$

Factor $5$ out of $5 (3 x^{2} - 7 x) + 5 (- 6)$ .

$5 (3 x^{2} - 7 x - 6)$

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 $a \cdot c = 3 \cdot - 6 = - 18$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$5 (3 x^{2} - 7 (x) - 6)$

Rewrite $- 7$ as $2$ plus $- 9$

$5 (3 x^{2} + (2 - 9) x - 6)$

Apply the distributive property.

$5 (3 x^{2} + 2 x - 9 x - 6)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$5 ((3 x^{2} + 2 x) - 9 x - 6)$

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

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

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

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

Remove unnecessary parentheses.

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

Factor 15x^2-35x-30

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