TITLE: How do I find the roots of this polynomial of degree $4$?
QUESTION [6 upvotes]: I am studying for finals and in the review packet is shown this problem:
$$P(x)=2x^4 + 5x^3 + 5x^2 + 20x - 12$$
I don't know what to do, I have already tried looking in the textbook and Khan academy.

REPLY [4 votes]: Have you heard of the rational root test?
It implies that rational roots to this are of the form $p/q$ where $p$ divides $12$ and $q$ divides $2$. There are only a few numbers like this so you can check them.
Once you have a few roots, you can divide and get a smaller polynomial that is easier to manage.