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Math Prize 2021 Problem 14

Source:

September 19, 2021
Math Prize for Girls

Problem Statement

Let SS be the set of monic polynomials in xx of degree 6 all of whose roots are members of the set {āˆ’1,0,1}\{ -1, 0, 1\}. Let PP be the sum of the polynomials in SS. What is the coefficient of x4x^4 in P(x)P(x)?
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