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Factor Theorem

Using factor ...

Question

Using factor theorem show $x - 2$ is a factor of $x^{6} - 64$

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Solution

Let $f (x) = x^{6} - 64$
By factor theorem, $x - R$ is a factor of $f (x)$ if and only if $f (R) = 0$ , here, $R = 2$ and $f (x) = f (2) = 2^{6} - 64 = - 64 = 0$
$\Rightarrow (x - 2)$ is a factor of $x^{6} - 64$

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