# linear algebra – nth roots of the unit

Let $$q$$ to be a primordial power and $$n$$ a positive integer at gcd (n, q) = 1.
Let $$E ^ {(n)}$$ be the whole of the nth roots of unity. For each positive integer $$d$$ such as $$d | n$$ , let $$Q_d (x): = prod _ { alpha in E ^ {(n)} \ {ord ( alpha) = d}} (x- alpha)$$

Why does it follow? $$x ^ n-1 = prod_ {d: d | n} Q_d (x)$$