Factor x^4-4x^3-64x+256

$x^{4} - 4 x^{3} - 64 x + 256$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

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

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

$x^{3} (x - 4) - 64 (x - 4)$

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

$(x - 4) (x^{3} - 64)$

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

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

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 $b = 4$ .

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

Factor.

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Simplify.

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

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

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

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

Remove unnecessary parentheses.

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

Combine exponents.

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Raise $x - 4$ to the power of $1$ .

${(x - 4)}^{1} (x - 4) (x^{2} + 4 x + 16)$

Raise $x - 4$ to the power of $1$ .

${(x - 4)}^{1} {(x - 4)}^{1} (x^{2} + 4 x + 16)$

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

${(x - 4)}^{1 + 1} (x^{2} + 4 x + 16)$

Add $1$ and $1$ .

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

Factor x^4-4x^3-64x+256