Factor x^3-2x^2-4x+8

$x^{3} - 2 x^{2} - 4 x + 8$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

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

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

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

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

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

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

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

Factor.

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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 $b = 2$ .

$(x - 2) ((x + 2) (x - 2))$

Remove unnecessary parentheses.

$(x - 2) (x + 2) (x - 2)$

Combine exponents.

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Raise $x - 2$ to the power of $1$ .

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

Raise $x - 2$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Factor x^3-2x^2-4x+8

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