show thatx-1 is a factor of x10-1and x11-1

Question

Its solution

Answer 1

To prove the factor, let each expression be set to zero:

x^10-1=0; so x^10=1 and x=1, because x^n=1 is x=1^(1/n)=1, or nth root of 1 is 1, no matter what value n is. ( because (1*1*1*..*1=1). Therefore, x=1 is also a solution of x^11-1. If x=1 is a solution, then x-1 must be a factor.