3. ​The graph of a higher order polynomial function may not intersect the x-axis. Use what you have learned in this lesson to describe the characteristics of a higher order (greater than degree 2) polynomial that will not intersect the x-axis.
1) Write the polynomial function in standard and factored form.
2) Sketch the graph of the polynomial function, labeling key points on the graph and describe its characteristics.
3) Describe how you know that graph will never intersect the x-axis.
4) Change the polynomial into a higher order polynomial that will intersect the x-axis and describe its characteristics.