IMO 1976 LL POL30

Prove that if P(x) = (x−a)kQ(x), where k is a positive integer,

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IMO 1976 LL POL30

Origin: POL

Problem

Prove that if P(x) = (x−a)kQ(x), where k is a positive integer, a is a nonzero real number, Q(x) is a nonzero polynomial, then P(x) has at least k + 1 nonzero coefficients.