Why is a rational number whose $p$-adic valuation less than $1$ not a $p$-adic integer?

Question

Let $\mathbb{Q}_p$ be the $p$-adic field with ring of integers $\mathbb{Z}_p$.

Consider a polynomial $f(x)=\frac{1}{4}(13x^5+121x^4+55x^2)$.

Each coefficient has $3$-adic absolute value $0$.

So it seems $f(x) \in \mathbb{Z}_3[x]$.

Am I missing something ?