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) $