This may seems to be an elementary question, but I found no answers on MO nor google.

I have always heard "polynomials are easier to handle with than integers". For example:

1. When $n$ is quite large, maybe 200 or more, it's relatively easier to factorize a polynomial $f$ of degeree $n$ than to factorize an integer with $n$ bytes.

2. When multiplying large integers, we see them as polynomials,use techniques such as FFT,intepolations to multiply polynomials,and then back to integers.

3.The zeta functions of $F[x]$ and $\mathbb{Z}$, and the former are easier to study than the latter.

Of course there are other examples, but because of my shortage of knowledge, I can only lise these above.

So my question is (as in the titile): Why are polynomials easier to handle with than integers? I ask this because contrary to our intuitives, polynomials are "more complex" objects than integers.