Imagine you are writing exam questions for an algebra course. You want to write questions that include finding the zeros of polynomials. To balance the difficulty level of the test’s questions, you decide to include two different types of questions, as described here:
- Question #1: A polynomial of degree at least 3 where all the zeros are positive whole numbers
- Question #2: A polynomial of degree at least 3 where one or more of the roots are fractions
Find two polynomials for the two described questions. Explain how you know each question satisfies the requirements stated. What approach did you use to find these polynomials?