Factor 9x^3+18x^2-x-2

$9 x^{3} + 18 x^{2} - x - 2$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 x^{3} + 18 x^{2}) - x - 2$

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

$9 x^{2} (x + 2) - (x + 2)$

Step 2

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

$(x + 2) (9 x^{2} - 1)$

Step 3

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

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

Step 4

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

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

Step 5

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 1$ .

$(x + 2) ((3 x + 1) (3 x - 1))$

Remove unnecessary parentheses.

$(x + 2) (3 x + 1) (3 x - 1)$