Factor 10x^2-5x-15

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

Step 1

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

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

$5 (2 x^{2}) - 5 x - 15$

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

$5 (2 x^{2}) + 5 (- x) - 15$

Factor $5$ out of $- 15$ .

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

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

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

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

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

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 $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

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

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$5 (2 x (x + 1) - 3 (x + 1))$

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

$5 ((x + 1) (2 x - 3))$

Remove unnecessary parentheses.

$5 (x + 1) (2 x - 3)$

Factor 10x^2-5x-15

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