1. Explain what synthetic division is. Illustrate with example. In synthetic division, what relationship does the divisor and remainder have to the original polynomial function, according to the Remainder Theorem?
2. What general characteristics for the graph of any polynomial function can be found by looking at its equation? What can you tell about the graph of a polynomial function by examining the leading coefficient? (Assume the polynomial is arranged in descending order.) What can you tell about the graph of a polynomial function by examining its highest power?
3. Finding the roots to non quadratic equations has always been a challenge. How are the roots, and where the graph crosses the x-axis, related to each other? Illustrate with example.