I have this problem:

Let $t$ be a root of the polynomial $f(x) = x³ + x² - 2x + 8$. Let $\phi = \displaystyle \frac{4}{t}$
and let $K = \mathbb{Q}(t)$.

I was able to show that $f(x)$ is irreducible, and that $\phi$ is in $O\_K$. However, I am not sure how to show that $\phi$ is not in $\mathbb{Z}[t]$.

Any help is appreciated.