Show that `(x-1)` is a factor of `x^(10)-1` and also of `x^(11)-1.`

Explanation

Let `p(x)=x^10−1` and `q(x)=x^11−1`
If `(x−1)` is factor of `x^10−1` and `x^11−1`,
Then the value of `p(x)=x^10−1` and `q(x)=x^11−1` is zero when `x−1=0` or `x=1`.
Replace `x` by `1` we get,
`p(x)=x^10−1`
`p(1)=(1)^10−1`
`p(1)=1−1=0`
`q(x)=x^11−1`
`q(1)=1−1=0`
So `p(1)` and `q(1)` are zero then `x−1` is a factor of `x^10−1` and `x^11−1`.