Q4 of 31 Page 245

In each pair of polynomials below find what kind of natural number n must be, so that the first is a factor of the second.

x + 1, xn + 1

Given, x + 1, xn + 1 pair of polynomials


Need to find out n such as first polynomial is factor of second


⇒ To check x + 1 is factor of xn + 1 we must get xn + 1 = 0 when substituted x with – 1 from the first polynomial


⇒ Consider n as 1 then the polynomial equation will be x + 1 which is equal to zero and x + 1 will is the factor.


We get, (– 1) + 1 = 0


∴ x + 1 is the factor of xn + 1


Hence, n = 1


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