Factor 15x^2-10x-5

$15 x^{2} - 10 x - 5$

Step 1

Factor $5$ out of $15 x^{2} - 10 x - 5$ .

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

$5 (3 x^{2}) - 10 x - 5$

Factor $5$ out of $- 10 x$ .

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

Factor $5$ out of $- 5$ .

$5 (3 x^{2}) + 5 (- 2 x) + 5 (- 1)$

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

$5 (3 x^{2} - 2 x) + 5 (- 1)$

Factor $5$ out of $5 (3 x^{2} - 2 x) + 5 (- 1)$ .

$5 (3 x^{2} - 2 x - 1)$

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 $a \cdot c = 3 \cdot - 1 = - 3$ and whose sum is $b = - 2$ .

Factor $- 2$ out of $- 2 x$ .

$5 (3 x^{2} - 2 (x) - 1)$

Rewrite $- 2$ as $1$ plus $- 3$

$5 (3 x^{2} + (1 - 3) x - 1)$

Apply the distributive property.

$5 (3 x^{2} + 1 x - 3 x - 1)$

Multiply $x$ by $1$ .

$5 (3 x^{2} + x - 3 x - 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$5 ((3 x^{2} + x) - 3 x - 1)$

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

$5 (x (3 x + 1) - (3 x + 1))$

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$5 ((3 x + 1) (x - 1))$

Remove unnecessary parentheses.

$5 (3 x + 1) (x - 1)$

Factor 15x^2-10x-5

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