Detecting whether a point is above or below a polynomial function

Question

I saw a lot of similar questions, but all regarding to the line and my problem is that I need to check whether the point is below or above a polynomial of degree 2, 3, 4 or 5. What I tried to do was just putting an $X_p$ (x from given point) into polynomial equation and check if its result is lower or greater than $Y_p$, but it's definitely not a correct way to do this. Any help appreciated!