Question

Which one of the following statements is correct?

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

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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