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

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

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 2

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

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

Step 3

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

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

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 $b = 3$ .

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

Remove unnecessary parentheses.

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