Factor x^3+6x^2-25x-150

$x^{3} + 6 x^{2} - 25 x - 150$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{3} + 6 x^{2}) - 25 x - 150$

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

$x^{2} (x + 6) - 25 (x + 6)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $x + 6$ .

$(x + 6) (x^{2} - 25)$

Step 3

Rewrite $25$ as $5^{2}$ .

$(x + 6) (x^{2} - 5^{2})$

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 $b = 5$ .

$(x + 6) ((x + 5) (x - 5))$

Remove unnecessary parentheses.

$(x + 6) (x + 5) (x - 5)$