Repeated Factors - Multiplicity
Multiplicity. Use the sliders to create different polynomials of different degrees.
Start with a small amount of factors, then increase the number of factors and number of repeated factors as your understanding increases. Try various combinations of the factors, including using a specific factor more than once in the same equation.
Think about the following questions as you increase the number of factors and number of repeated factors:
1. How does the degree of the polynomial effect the number of roots in the equation?
2. What is the difference between the graphs of even and odd degree polynomials?
3. What effect does using a factor more than once in the same equation have on the graph of that equation?
4. Look at the multiplicity of a given factor. How do an even or odd multiplicity change how it touches or crosses the x-axis?