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Question

Using factor theorem, show that $$g(x)$$ is a factor of $$p(x)$$, when $$p(x)=x^4-x^2-12$$, $$g(x)=x+2$$.


Solution

The given polynomial is 
$$p(x)=x^4-x^2-12$$
and $$g(x)=x+2$$

Now,
$$g(x)=0$$
$$\Rightarrow x+2=0$$
$$\Rightarrow x=-2$$

If, $$(x+2)$$ is a factor of $$p(x)$$, then $$p(-2)=0$$
Putting, $$x=-2$$
$$p(-2)=(-2)^4-(-2)^2-12$$
            $$=16-4-12$$
            $$=0$$

Hence, $$(x+2)$$ is a factor of $$p(x)$$.

Mathematics
RS Agarwal
Standard IX

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