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  • . If xn -1 is divisible by x -k, then the least positive integral value of k is A. 1 B. 2 C. 3 D. 4

If x^n – 1 is divisible byx - k , then the least positive integral value of k is
A. 1
B. 2
C. 3
D. 4

Answers (1)

The answer is the option (A) 1

Given:

P(n) = x^n – 1 is divisible byx - k

Now, we’ll substitute different values for n,

At n = 1,

P(1) = x -1

At n = 2,

P(2) = x^2 -1

           = (x -1) (x + 1)

At n = 3,

P(3) = x^3 -1

           = (x -1) (x^2 + xy + 1)

At n = 4,

\\P(4) = x^4 -1\\ = (x^2 -1) (x^2 + 1) \\ = (x -1) (x + 1) (x^2 + 1)
          

Therefore, ‘1’ is the least possible integral value of k.

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infoexpert21

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