Question

How to show that x-1 is a factor of x^10-1 and also of x^11-1

Answer 1

let x-1 is a factor of x^10-1 and  x^11-1

using remainder thearom :

x-1 = 0

x = 1

f(x) = x^10-1                    and       p(x) = x^11-1

f(1) = (1)^10-1                  and       p(1) = (1)^11 - 1

1-1 = 0                             and          1-1=0

hence , remainder is zero  x-1 is a factor of x^10-1 and  x^11-1