Exercise 1. Consider the following polynomials in P P(x) = x4 + 2; P(x) = x...

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Exercise 1. Consider the following polynomials in P P(x) = x4 + 2; P(x) = x +2: P3(x) = x + x +2+2; Determine whether there exists a linear function f : P Z such that - [8]; [!] f(p(x)) = f(p(x)) = f(p3(x)) = S(p(x)) = f(ps(x)) = P(x) = 2x + x + x +1; Ps(x) = 2x +1. [H]; Exercise 1. Consider the following polynomials in P P(x) = x4 + 2; P(x) = x +2: P3(x) = x + x +2+2; Determine whether there exists a linear function f : P Z such that - [8]; [!] f(p(x)) = f(p(x)) = f(p3(x)) = S(p(x)) = f(ps(x)) = P(x) = 2x + x + x +1; Ps(x) = 2x +1. [H];