Daniel J Smith Custom TMUA alpha · Question 15

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Daniel J Smith Custom TMUA alpha · Q15

Logic & proofNumber & countingAlgebra

Consider the following statement about a polynomial $p(x)$ with real coefficients:

$(*)$ If $p(n)$ is even for every integer $n$ , then every coefficient of $p(x)$ is even.

Which one of the following is a counterexample to $(*)$ ?

p(x)=x^2+x

p(x)=2x^2+4

p(x)=2x^2+x

p(x)=4x^3+2x

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