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Let $f(x)$ be a quadratic polynomial such that $f(-4) = -22,$ $f(-1)=2$, and $f(2)=-1.$ Let $g(x) = f(x)^{16}.$ Find the sum of the coefficients of the terms in $g(x)$ with even exponents. (For example, the sum of the coefficients of the terms in $-7x^3 + 4x^2 + 10x - 5$ with even exponents is $(4) + (-5) = -1.$)

 Aug 29, 2020
edited by RichardRusczyk  Aug 29, 2020
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The sum of the coefficient is (3^4 + 1^4)/2 = 41.

 Aug 29, 2020

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