The factors of $x^{3} - 64$ are ______________.

(x - 3) a n d (x^{2} + 3 x + 9)

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

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(x + 3) a n d (x^{2} + 4 x + 16)

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(x + 4) a n d (x^{2} - 4 x - 16)

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Solution

The correct option is B $(x - 4) (x^{2} + 4 x + 16)$
Given $x^{3} - 64$ = $x^{3} - 4^{3}$
We know that $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
Here, the given question is of the form $a^{3} - b^{3}$ , where $a = x$ and $b = 4$ .
$∴$ $x^{3} - 4^{3} = (x - 4) (x^{2} + 4 x + 4^{2})$
$= (x - 4) (x^{2} + 4 x + 16)$

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