Write as a Set of Linear Factors x^3-2x^2-9x+18=0

$x^{3} - 2 x^{2} - 9 x + 18 = 0$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{3} - 2 x^{2}) - 9 x + 18 = 0$

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

$x^{2} (x - 2) - 9 (x - 2) = 0$

Step 2

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

$(x - 2) (x^{2} - 9) = 0$

Step 3

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

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

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 $b = 3$ .

$(x - 2) ((x + 3) (x - 3)) = 0$

Remove unnecessary parentheses.

$(x - 2) (x + 3) (x - 3) = 0$