Math 116: Chapter 4 Polynomial Quiz

This quiz is worth 20 points. The in-class portion of the exam is worth 80 points.

• You are to write the answers on the cover page and attach all work. Do not recopy your work when trying possible rational zeros and include only those which work. I want to see all of the numbers you tried.
• You may work in groups of up to three people. Each person in the group is to turn in an exam.
• There are ten possible polynomial functions. Each group will have a different function

How many real or complex solutions will there be to f (x) = 0?

1. List all possible combinations of the number of total, positive, negative, and complex solutions to f (x) = 0.
2. List all possible rational solutions to f (x) = 0.
3. Find all real or complex solutions to f (x) = 0.
4. Completely factor f (x) using linear real or complex factors.
5. Completely factor f (x) using linear and irreducible quadratic real factors.
6. Sketch the graph of y = f (x).

Consider the polynomial function f defined by:

Hints

• There is at least one non-integer rational answer.
• There are at least two non-rational answers.
• There is at least one repeated root.