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Mathematics, 06.03.2021 20:00 10040816

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1. Let f(x) = x^{4} -3x^{2} +2 and g(x) = 2x^{4} -6x^2+2x-1. Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b · g(x)?

2. Suppose f is a polynomial such that f(0) = 47, f(1) = 32, f(2) = -13, and f(3)=16. What is the sum of the coefficients of f?

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