Factor f(x)=x^3+2x^2-4x-8

$f (x) = x^{3} + 2 x^{2} - 4 x - 8$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$f (x) = (x^{3} + 2 x^{2}) - 4 x - 8$

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

$f (x) = x^{2} (x + 2) - 4 (x + 2)$

Step 2

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

$f (x) = (x + 2) (x^{2} - 4)$

Step 3

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

$f (x) = (x + 2) (x^{2} - 2^{2})$

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 $a = x$ and $b = 2$ .

$f (x) = (x + 2) ((x + 2) (x - 2))$

Remove unnecessary parentheses.

$f (x) = (x + 2) (x + 2) (x - 2)$

Step 5

Combine exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (x) = {(x + 2)}^{1 + 1} (x - 2)$

Add $1$ and $1$ .

$f (x) = {(x + 2)}^{2} (x - 2)$