Here is the question I am trying to attempt:

[![enter image description here](https://i.stack.imgur.com/cqaXT.png)](https://i.stack.imgur.com/cqaXT.png)

I feel like there is a typo... it says let $p(x)=a\_{n}x^{n}$. Shouldn't it be $p(x) = a\_{n}^{n}\cdots + a\_{1}x+a\_{0}$? I feel like I must use the roots of $p(x)$ in my answer, but I am not sure how and where. Any hints on what I should do?

Edit: The duplicate answer did not help me because I am trying to prove injectivity...it has already been assumed that $\eta$ is a ring homomorphism.