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


⇒ since, when x is substituted with 1 it will satisfy irrespective of n in the given polynomial


Consider n as 1 then the polynomial equation itself wiil be x – 1 and x – 1 will be the factor


Hence, n is 1


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