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1. 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 $g(x)$ 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 $(4) + (-5) = -1.$)

 Apr 8, 2020
 #1
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I believe I posted an answer to your first question already. You can find the solution here:

https://web2.0calc.com/questions/reposted-again-bc-a-certain-user-kept-complaining#r7

let me know if you see anything wrong with my solution, and I'll do my best to correct it.

 

Also, don't repost your question after it hasn't been answered for an hour or two. That's unnecessary. There just may not be people on at this time.

 Apr 8, 2020
edited by jfan17  Apr 8, 2020
 #3
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Hi jfan17,

Your solution is really wonderful one! 

I just have one question,

why did you plug 1 and -1 in the last steps (I.e. g(1) and g(-1) ?)

Guest Apr 8, 2020
 #4
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If you look back to my soltuion, that allows me to add the two equations and cancel out all the odd terms. That's because when you substitute -1 for all the x values, the ones with all odd powers of x(x^1, x^3, etc.) will be negative, so when you add it with f(1), you get the even coefficients. Great question!

jfan17  Apr 11, 2020
 #2
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OMG THANKYOU

 Apr 8, 2020

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