Algebra Examples

$s (x) = x^{4} + 4 x^{3} - 64 x - 256$

Step 1

Factor out the greatest common factor from each group.

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Step 1.1

Group the first two terms and the last two terms.

$s (x) = (x^{4} + 4 x^{3}) - 64 x - 256$

Step 1.2

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

$s (x) = x^{3} (x + 4) - 64 (x + 4)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $x + 4$ .

$s (x) = (x + 4) (x^{3} - 64)$

Step 3

Rewrite $64$ as $4^{3}$ .

$s (x) = (x + 4) (x^{3} - 4^{3})$

Step 4

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 4$ .

$s (x) = (x + 4) ((x - 4) (x^{2} + x \cdot 4 + 4^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Move $4$ to the left of $x$ .

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

Step 5.1.2

Raise $4$ to the power of $2$ .

$s (x) = (x + 4) ((x - 4) (x^{2} + 4 x + 16))$

Step 5.2

Remove unnecessary parentheses.

$s (x) = (x + 4) (x - 4) (x^{2} + 4 x + 16)$