Question

Verify that x-1 is a factor of x^(n) - 1

Answer 1

if x-a is the factor of f(x)
then f(a) = 0
now put x=1 in
x^n-1
and see whether u get answer as 0.

Answer 2

put x=1 in above equation and if it reduces to zero then thats the factor

Answer 3

x^n - 1 = (x-1)(1 + x + x^2 +...+ x^n-1)

Would you say that this is a good verification?

Answer 4

It just seemed too easy to me previously lol

Answer 5

yup, that verification will also do.
just put there x=1
so (1-1)(....) = 0(...) = 0

Answer 6

Got it! Thank you!

Answer 7

welcome :)