Polynomials with even constant term

#ring_theory

Let $I \subseteq Z [x]$ denote the set of all polynomials with even constant term.
(a) Prove that $I$ is an ideal.
(b) Prove that $I$ is not a principal ideal.

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L A T E X

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Let $I\subseteq {\bf Z}[x]$ denote the set of all polynomials with even constant term.
\begin{enumerate}[label=\alph*)]
	\item Prove that $I$ is an ideal.
	\item Prove that $I$ is not a {\itshape principal} ideal.
\end{enumerate}