Factor -3x^2-17x-10

$- 3 x^{2} - 17 x - 10$

Step 1

Factor $- 1$ out of $- 3 x^{2} - 17 x - 10$ .

Factor $- 1$ out of $- 3 x^{2}$ .

$- (3 x^{2}) - 17 x - 10$

Factor $- 1$ out of $- 17 x$ .

$- (3 x^{2}) - (17 x) - 10$

Rewrite $- 10$ as $- 1 (10)$ .

$- (3 x^{2}) - (17 x) - 1 (10)$

Factor $- 1$ out of $- (3 x^{2}) - (17 x)$ .

$- (3 x^{2} + 17 x) - 1 (10)$

Factor $- 1$ out of $- (3 x^{2} + 17 x) - 1 (10)$ .

$- (3 x^{2} + 17 x + 10)$

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 $a \cdot c = 3 \cdot 10 = 30$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$- (3 x^{2} + 17 (x) + 10)$

Rewrite $17$ as $2$ plus $15$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Remove unnecessary parentheses.

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

Factor -3x^2-17x-10

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