Note that you will be graded not only on the accuracy of your final answer but also on the methods you use to reach the answer, so be sure to show all of your work and explain your reasoning carefully. If you need graph paper, download and print it from MathBits. Don't just copy the graph from a calculator or a computer algebra system!

For each of the following 3 polynomials, do all of the following:

1. Write the problem and its number on your page. Be sure to have clear problem numbers, answers, and the corresponding work for EACH problem in order.
2. List all of the possible rational roots.
3. Then use synthetic division to test the possible rational roots and factor as far as possible.
4. Identify complex roots, if any.
5. Sketch a careful graph of the function. You must:
   • correctly show the end behavior
   • the shape of the graph near x-intercepts
   • (if relevant) anything you can learn by considering symmetry and transformations Problems: 1) p(x)= 2x^4-3x^3-6x^2+5x+6
   • 2) p(x)= x^4+4x^3+13x^2+36x+36
   • 3) p(x)= 2x^5-9x^4+6x^3+22x^2-20x-25 RUBRIC: Provided all parts of ALL THE PROBLEMS with 0-2 errors: (1)listed all possible rational roots (2) Use synthetic division to test possible rational roots and factor as far as possible (3) identify complex roots (if any) (4) correctly show end behavior (5) the shape of the graph near the x-intercept (6) if relevant: anything learned by considering symmetry and transformations Properly used all math conventions required for these problems. Student submitted work in a clear and orderly fashion that was easy to read and follow.