How do you simplify (x^10) - 1 / (x - 1)?
(x^10) - 1 / (x - 1)
You know that if f(x) = x^10 - 1
f(1 = 1-1 = 0
so x-1 is a factor and the division will be exact
Do either a long algebraic division or a synthetic division to show that
(x^10) - 1 / (x - 1)
= x^9 + x^8 + x^7 + .... + x^2 + x + 1