Lesson Plan: Upper and Lower Bound Tests for Polynomial Functions
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use upper and lower bound tests to verify if the given interval is the interval that contains all real zeros.
Objectives
Students will be able to
- determine if a rational root is possible and list the possible rational roots of a given polynomial using the rational zeros theorem,
- apply the rational zeros theorem and the upper and lower bound tests to determine if a given interval must contain all of the roots of a given polynomial,
- apply the upper and lower bound tests along with synthetic division to find all the roots of a polynomial.
Prerequisites
Students should already be familiar with
- polynomials and roots,
- factoring quadratics,
- synthetic divisions,
- zeros of polynomial functions.
Exclusions
Students will not cover
- graphing general polynomial functions,
- Descartes’s rule of sign changes.
