Write as a Set of Linear Factors f(x)=x^3-512

$f (x) = x^{3} - 512$

Rewrite $512$ as $8^{3}$ .

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

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 $b = 8$ .

$f (x) = (x - 8) (x^{2} + x \cdot 8 + 8^{2})$

Simplify.

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Move $8$ to the left of $x$ .

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

Raise $8$ to the power of $2$ .

$f (x) = (x - 8) (x^{2} + 8 x + 64)$

Write as a Set of Linear Factors f(x)=x^3-512

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