We haven't simplified our polynomial in degree, but it's nice not to carry around large coefficients.
In physics and chemistry particularly, special sets of named polynomial functions like LegendreLaguerre and Hermite polynomials thank goodness for the French! Features of a polynomial graph End behavior: odd degree Here are the graphs of two cubic polynomials.
But you can't factor this expression using the real numbers you're used to. But the process for finding polynomials from their zeroes works the same as for finding quadratics from their zeroes. Each turning point represents a local minimum or maximum. That's far beyond the scope of your current math practice, so for now it's enough to note that you have two real roots 2 and -2and two imaginary roots that you'll leave undefined.
Here is a table of those algebraic features, such as single and double roots, and how they are reflected in the graph of f x. They are the points at which the graph of f x crosses or touches the x-axis.
So now we know the degree, how to solve?