Factor x^3+2x^2-x-2=0

$x^{3} + 2 x^{2} - x - 2 = 0$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{3} + 2 x^{2}) - x - 2 = 0$

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

$x^{2} (x + 2) - (x + 2) = 0$

Step 2

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

$(x + 2) (x^{2} - 1) = 0$

Step 3

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

$(x + 2) (x^{2} - 1^{2}) = 0$

Step 4

Factor.

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 $b = 1$ .

$(x + 2) ((x + 1) (x - 1)) = 0$

Remove unnecessary parentheses.

$(x + 2) (x + 1) (x - 1) = 0$