## 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?

- List all possible combinations of the number of total, positive, negative, and complex
solutions to
*f* (*x*) = 0.
- List all possible rational solutions to
*f* (*x*) = 0.
- Find all real or complex solutions to
*f* (*x*) = 0.
- Completely factor
*f* (*x*) using linear real or complex factors.
- Completely factor
*f* (*x*) using linear and irreducible quadratic real factors.
- 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.