Write as a Set of Linear Factors x^3+5x^2-9x-45

$x^{3} + 5 x^{2} - 9 x - 45$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{3} + 5 x^{2}) - 9 x - 45$

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

$x^{2} (x + 5) - 9 (x + 5)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $x + 5$ .

$(x + 5) (x^{2} - 9)$

Step 3

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

$(x + 5) (x^{2} - 3^{2})$

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 $b = 3$ .

$(x + 5) ((x + 3) (x - 3))$

Remove unnecessary parentheses.

$(x + 5) (x + 3) (x - 3)$