= Solution
Suppose $X=f_1\cdots f_s$ were a product of <irreducible elements> of $R$. Since <degree of a polynomial> is additive under products, exactly one factor has positive degree and all the others are constant. By the preceding classification, the positive-degree factor has constant term $\pm1$, while every constant irreducible is $\pm p$ for a prime $p$. Their product therefore has a nonzero constant term, contradicting $X(0)=0$.
Thus \b[$X$ is not a product of irreducibles], so this <integral domain> is not an <atomic domain> and in particular is not a <unique factorization domain>.
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