Factor 4x^3+8x^2-9x-18

$4 x^{3} + 8 x^{2} - 9 x - 18$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{3} + 8 x^{2}) - 9 x - 18$

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

$4 x^{2} (x + 2) - 9 (x + 2)$

Step 2

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

$(x + 2) (4 x^{2} - 9)$

Step 3

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

Step 4

Rewrite $9$ as $3^{2}$ .

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

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 $a = 2 x$ and $b = 3$ .

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

Remove unnecessary parentheses.

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