Divide (x^3+2x^2-x-2)÷(x+2)

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

Rewrite the division as a fraction.

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

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Rewrite $1$ as $1^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Divide $(x + 1) (x - 1)$ by $1$ .

$(x + 1) (x - 1)$

Expand $(x + 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$x (x - 1) + 1 (x - 1)$

Apply the distributive property.

$x \cdot x + x \cdot - 1 + 1 (x - 1)$

Apply the distributive property.

$x \cdot x + x \cdot - 1 + 1 x + 1 \cdot - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 1 + 1 x + 1 \cdot - 1$

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x + 1 x + 1 \cdot - 1$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x + 1 x + 1 \cdot - 1$

Multiply $x$ by $1$ .

$x^{2} - x + x + 1 \cdot - 1$

Multiply $- 1$ by $1$ .

$x^{2} - x + x - 1$

Add $- x$ and $x$ .

$x^{2} + 0 - 1$

Add $x^{2}$ and $0$ .

$x^{2} - 1$