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

2.Let $$f(x) = x^4-3x^2 + 2$$ and $$g(x) = 2x^4 - 6x^2 + 2x -1$$. Let $$a$$ be a constant. What is the largest possible degree of $$f(x) + a\cdot g(x)$$?

Thanks a billion!

-PharaoCarl

Apr 8, 2020
edited by PharaoCarl  Apr 8, 2020

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