Lesson: Upper and Lower Bound Tests for Polynomial Functions Mathematics • 12th Grade

In this lesson, we will learn how to use upper and lower bound tests to verify if the given interval is the interval that contains all real zeros.

Lesson Plan

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.

Q1:

Using synthetic division and the upper and lower bound tests, find all real zeros of the function .

Q2:

Hannah is trying to find zeros in the function . She has used synthetic division to find for , , 1, and 3.

Use her results to state an interval in which all real zeros of lie.

Q3:

Consider the function .

James is using synthetic division to help him find real zeros of .

What can he conclude about −5?

What can he conclude about 2?

Find all the real zeros of .