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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 \((4) + (-5) = -1.\))

 

Please include a full explanation if you can, thank you! :)

 Sep 2, 2020
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The sum of the coefficient is 3^16.

 Sep 3, 2020

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