Divide (12x^2-10x-12)÷(3x+2)

$(12 x^{2} - 10 x - 12) \div (3 x + 2)$

Step 1

Rewrite the division as a fraction.

$\frac{12 x^{2} - 10 x - 12}{3 x + 2}$

Step 2

Simplify the numerator.

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

Factor $2$ out of $12 x^{2}$ .

$\frac{2 (6 x^{2}) - 10 x - 12}{3 x + 2}$

Factor $2$ out of $- 10 x$ .

$\frac{2 (6 x^{2}) + 2 (- 5 x) - 12}{3 x + 2}$

Factor $2$ out of $- 12$ .

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

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

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

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

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

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 $a \cdot c = 6 \cdot - 6 = - 36$ and whose sum is $b = - 5$ .

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

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

Rewrite $- 5$ as $4$ plus $- 9$

$\frac{2 (6 x^{2} + (4 - 9) x - 6)}{3 x + 2}$

Apply the distributive property.

$\frac{2 (6 x^{2} + 4 x - 9 x - 6)}{3 x + 2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{2 ((6 x^{2} + 4 x) - 9 x - 6)}{3 x + 2}$

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

$\frac{2 (2 x (3 x + 2) - 3 (3 x + 2))}{3 x + 2}$

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

$\frac{2 ((3 x + 2) (2 x - 3))}{3 x + 2}$

$\frac{2 (3 x + 2) (2 x - 3)}{3 x + 2}$

Step 3

Cancel the common factor of $3 x + 2$ .

Cancel the common factor.

$\frac{2 (3 x + 2) (2 x - 3)}{3 x + 2}$

Divide $2 (2 x - 3)$ by $1$ .

$2 (2 x - 3)$

Step 4

Apply the distributive property.

$2 (2 x) + 2 \cdot - 3$

Step 5

Multiply $2$ by $2$ .

$4 x + 2 \cdot - 3$

Step 6

Multiply $2$ by $- 3$ .

$4 x - 6$

Divide (12x^2-10x-12)÷(3x+2)

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