Kansas Algebra Program

Unit 5 Exam Objectives - Polynomial and Rational Functions

1. Form a polynomial function, given some zeros and their multiplicities, and write the function in expanded form.
2. Find the intercepts and asymptotes (vertical, horizontal, and oblique) for a given rational function.
3. Analyze a rational function and use the information to make a careful hand drawn sketch.
4. Determine if the graph of a rational function has any holes or intersects a horizontal or oblique asymptote.
5. Use synthetic division with polynomials with the divisor in the form (x - r).
6. Use long division with polynomials.
7. Identify the potential rational zeros of a polynomial function.
8. Understand and use the remainder, factor, and rational zeros theorems.
9. Determine if a given binomial is a factor of a given polynomial.
10. Find all the real and complex zeros for a polynomial function.
11. Write a polynomial function in a specified factored form (e.g. over the real numbers with integer coefficients, with linear factors, etc.).
12. Use a sign test and graph to solve polynomial and rational inequalities.