Graphical Behavior
Real Zeros
In the study of polynomial equations, the most important thing to understand is what "solution of an equation" means, because equations of higher degree allow for many solutions. The maximum number of solutions allowable is the degree of the polynomial. When a polynomial function is set equal to zero, another name for those solutions is zeros or roots.
The zeros of a polynomial are also the x-intercepts of the graph. x-intercepts can either cross the x-axis or they can just touch the x-axis without actually crossing the axis as you can see in the graphs below.
