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Question

Which one of the following statements is correct?


A
If x6+1 is divided by x+1, then the remainder is 2
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B
If x6+1 is divided by x1, then the remainder is 2
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C
If x6+1 is divided by x+1, then the remainder is 1
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D
If x6+1 is divided by x1, then the remainder is 1
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Solution

The correct option is B If $$x^{6} + 1$$ is divided by $$x - 1$$, then the remainder is $$2$$
By the remainder theorem,
If $$(x - \alpha)$$ divides $$f(x)$$ then $$f(\alpha)$$ is the remainder.
$$\therefore$$ if $$x^{6} + 1$$ is divided by $$(x - 1)$$ then,
Remainder $$= f(1) = 1^6+1$$
                                 $$=2$$

Mathematics

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