Question

Show that (x-1) is a factor of x¹⁰-1​

Answer 1

x^10 - 1 = (x^5+1)(x^5-1)
= (x^5+1)(x)(x^2+1)(x^2-1)
= (x^5+1)(x)(x^2+1)(x+1)(x-1)

See that (x-1) is one of the factors after the factorization. This proves it.
Whew

Answer 2

The answer is 0 X=1

1. x10-1

(1)10-1

1-1

=0

2. x11-1

(1)11-1

1-1

=0

Explanation: