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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.)

Nov 18, 2020

#6
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Variants of this question keep popping up!

Nov 19, 2020

#1
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Find the link and post it.

Nov 18, 2020
#2
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I did? Sorry! Ok, I will try to find it.....

After a lot of searching, I still can't find it! Did you see it, Melody?

Guest Nov 18, 2020
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(BTW, wasn't me! someone else posted it)

Guest Nov 18, 2020
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Thanks guest :)

Melody  Nov 19, 2020
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Well I asked questions on that previous post.

I will admit up front that I have not finished the question.

Finding f(x) is not super difficult but I did not finish the next step.

Maybe there is a nice short cut.

have you found f(x) yet?

Nov 19, 2020
#6
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Variants of this question keep popping up!

Alan Nov 19, 2020
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Thanks Alan,

I never would have thought of that  g(1)  and   g(-1) method

Melody  Nov 19, 2020
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Thanks Alan and Melody! That's really smart to substitute x=1 since that cancels the variables! Thanks so much!!!

Guest Nov 19, 2020