This post is used to collate any questions / uncertainties that you may have about Polynomials. Mentors will be looking in on this page, and providing explanations to help you understand. Do not be afraid to ask questions, as there will also be others with similar questions.
If you have a question, start a new comment and ask just that question (you can include related questions). State what you have done, and what you are having trouble with. Do not mix questions across different areas.
As an example,
I was working on question 5 and I got stuck. I can use rational root theorem to show that it has no rational roots. However, I do not know how to show that it has no real roots. Can someone guide me?