What does the degree of a polynomial expression tell you about its related polynomial function? Explain your thinking. Give an example of a polynomial expression of degree three. Provide information regarding the graph and zeros of the related polynomial function.

The graph of function like that may may never cross the x-axis,

so the function could have no real zeros.

If it does have zeros, they will come in pairs,

because "what goes up must come down" and vice versa.

Of course the function cannot have more zeros than its degree.

For example, a polynomial function of degree 6 could have 0, 2, 4, or 6 real zeros.