Factor x^3+3x^2-16x-48

$x^{3} + 3 x^{2} - 16 x - 48$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{3} + 3 x^{2}) - 16 x - 48$

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

$x^{2} (x + 3) - 16 (x + 3)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $x + 3$ .

$(x + 3) (x^{2} - 16)$

Step 3

Rewrite $16$ as $4^{2}$ .

$(x + 3) (x^{2} - 4^{2})$

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 $b = 4$ .

$(x + 3) ((x + 4) (x - 4))$

Remove unnecessary parentheses.

$(x + 3) (x + 4) (x - 4)$