Factor n^3+5n^2-4n-20

$n^{3} + 5 n^{2} - 4 n - 20$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(n^{3} + 5 n^{2}) - 4 n - 20$

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

$n^{2} (n + 5) - 4 (n + 5)$

Step 2

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

$(n + 5) (n^{2} - 4)$

Step 3

Rewrite $4$ as $2^{2}$ .

$(n + 5) (n^{2} - 2^{2})$

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 $a = n$ and $b = 2$ .

$(n + 5) ((n + 2) (n - 2))$

Remove unnecessary parentheses.

$(n + 5) (n + 2) (n - 2)$