# Study Guide - Chapter 4

## Math 116

1. Sketch the graph of a polynomial function. Four parts. Pay attention to the behavior on the left and right sides and at each intercept. Four parts.
2. Find a polynomial function with integer coefficients which has the indicated roots. Remember, square roots come in pairs and complex numbers come in pairs. Look at problems 27 - 36 in section 4.5. Three parts.
3. Use synthetic division to evaluate a polynomial function.
4. Given a seventh degree polynomial. List all combinations of positive, negative, and complex zeros and list all possible rational zeros.
5. Give a polynomial function which matches the graph shown.
6. Given a polynomial function and a value of x, state either the upper bound theorem or the lower bound theorem (whichever is appropriate) in everyday language. Then use the theorem to see if the value of x is a bound. Look at problems 17 - 20 in section 4.4.
7. Given one root of a cubic function, find the other two roots, and completely factor the function using linear and irreducible quadratic factors.

None of the problems on this exam are straight from the textbook. The in-class portion of the exam is worth 75 points.

The remainder of the exam is take home, is due on Friday, October 6, and is worth 25 points.

For the polynomial given you in class, you need to find the following.

1. List all possible combinations of positive, negative, and complex zeros. (5 points)
2. List all possible rational zeros. (5 points)
3. Find all zeros. (5 points)
4. Give the linear factorization for the polynomial. (3 points)
5. Give the factorization using linear and irreducible quadratic factors. (2 points)
6. Sketch the polynomial. (5 points)