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Factorisation of Polynomial

Question

Using factor theorem, show that $$g(x)$$ is a factor of $$p(x)$$, when $$p(x)=x^3-8$$, $$g(x)=x-2$$.

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Solution

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use factor theorem,

$$g(x)=x-2=0$$

$$x=2$$

$$p(x)=x^3-8$$

$$=(2)^3-8$$

$$=8-8=0$$

$$g(x)$$ is a factor of $$p(x)$$

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