Factor -10x^2-23x-12

$- 10 x^{2} - 23 x - 12$

Step 1

Factor $- 1$ out of $- 10 x^{2} - 23 x - 12$ .

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

$- (10 x^{2}) - 23 x - 12$

Factor $- 1$ out of $- 23 x$ .

$- (10 x^{2}) - (23 x) - 12$

Rewrite $- 12$ as $- 1 (12)$ .

$- (10 x^{2}) - (23 x) - 1 (12)$

Factor $- 1$ out of $- (10 x^{2}) - (23 x)$ .

$- (10 x^{2} + 23 x) - 1 (12)$

Factor $- 1$ out of $- (10 x^{2} + 23 x) - 1 (12)$ .

$- (10 x^{2} + 23 x + 12)$

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 $a \cdot c = 10 \cdot 12 = 120$ and whose sum is $b = 23$ .

Factor $23$ out of $23 x$ .

$- (10 x^{2} + 23 (x) + 12)$

Rewrite $23$ as $8$ plus $15$

$- (10 x^{2} + (8 + 15) x + 12)$

Apply the distributive property.

$- (10 x^{2} + 8 x + 15 x + 12)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((10 x^{2} + 8 x) + 15 x + 12)$

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

$- (2 x (5 x + 4) + 3 (5 x + 4))$

Factor the polynomial by factoring out the greatest common factor, $5 x + 4$ .

$- ((5 x + 4) (2 x + 3))$

Remove unnecessary parentheses.

$- (5 x + 4) (2 x + 3)$

Factor -10x^2-23x-12

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