1. Explain what synthetic division is and what it is used for. (include at least 2 different uses for synthetic division) Give an example of synthetic division, show all steps. Explain what your answer means.
2. Pick a cubic function. (use something not too simple. a good example: y = 2(x+1)^3 - 5) Starting with y = x^3, use vertical and horizontal translations, as well as, shrinking and stretching to graph your function. (make sure to explain in English what you are doing as well as graphing y = x^3 and your function) Using an algebraic method, find the roots of your function. Describe the symmetry of your function. Explain the concept of symmetry in general. (which functions are symmetric, which are not. how can you tell from the equation?)
3. State and explain (in simple english) what Remainder and Factor Theorems mean.
A step step explanation are provided for synthetic division, graphing cubic functions using transformations, and remainder factor theorem.