Divide (6x^2-9x-6)÷(x-2)

$(6 x^{2} - 9 x - 6) \div (x - 2)$

Rewrite the division as a fraction.

$\frac{6 x^{2} - 9 x - 6}{x - 2}$

Simplify the numerator.

Factor $3$ out of $6 x^{2} - 9 x - 6$ .

Factor $3$ out of $6 x^{2}$ .

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

Factor $3$ out of $- 9 x$ .

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

Factor $3$ out of $- 6$ .

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

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

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

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

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

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 $a \cdot c = 2 \cdot - 2 = - 4$ and whose sum is $b = - 3$ .

Factor $- 3$ out of $- 3 x$ .

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

Rewrite $- 3$ as $1$ plus $- 4$

$\frac{3 (2 x^{2} + (1 - 4) x - 2)}{x - 2}$

Apply the distributive property.

$\frac{3 (2 x^{2} + 1 x - 4 x - 2)}{x - 2}$

Multiply $x$ by $1$ .

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$\frac{3 (x (2 x + 1) - 2 (2 x + 1))}{x - 2}$

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$\frac{3 ((2 x + 1) (x - 2))}{x - 2}$

$\frac{3 (2 x + 1) (x - 2)}{x - 2}$

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{3 (2 x + 1) (x - 2)}{x - 2}$

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

$3 (2 x + 1)$

Apply the distributive property.

$3 (2 x) + 3 \cdot 1$

Multiply $2$ by $3$ .

$6 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$6 x + 3$

Divide (6x^2-9x-6)÷(x-2)

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