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Non-zero coeficients

Source: Brazilian Olympic Revenge 2020, P1

February 1, 2020
olympic revengeBrazilalgebra

Problem Statement

Let nn be a positive integer and a1,a2,…,ana_1, a_2, \dots, a_n non-zero real numbers. What is the least number of non-zero coefficients that the polynomial P(x)=(x−a1)(x−a2)⋯(x−an)P(x) = (x - a_1)(x - a_2)\cdots(x - a_n) can have?
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