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Practice problem

Every Function Is a Sum of Even and Odd Components

By Victor Wang
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If f(x)=x5+x4+x3+x2+x+1f(x) = x^5 + x^4 + x^3 + x^2 + x + 1 (a polynomial of degree 5), what is the degree of the even part f(x)+f(−x)2\frac{f(x)+f(-x)}{2} of ff?

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