# Section 4.5: Analysis

This section seems to be a quick abstract way to explain how one can tell whether or not a given polynomial is reducible in either $\mathbb{Q}$ or $\mathbb{Z}$. Hungerford starts with the Rational Root Test and later Eisenstein’s Criterion. This entire section is limited to $\mathbb{Q}$ and $\mathbb{Z}$, I wonder if there exists similar tests that are valid for other fields ($\mathbb{Z}$ is not a field but $\mathbb{Q}$ is). Yet, part of the power of what has been done so far comes from understanding how the basics of the areas of mathematics that have been taught to each of us since an early age (addition, division, multiplication etc). Whether or not there are similar tests won’t matter if the basics aren’t understood.