Analyzing the Multiplicity of Roots and Sign Changes in Functions

The video tutorial explains how the multiplicity of roots in a polynomial affects the sign changes of the function. It covers the intermediate value theorem, testing intervals for sign changes, and the behavior of double roots. The tutorial also discusses how multiplicity influences the end behavior of polynomials, providing a comprehensive understanding of these mathematical concepts.

What is the relationship between the roots of a polynomial and its factors?

What happens to the sign of a polynomial function at an even root compared to an odd root?

Illustrate how the zeros of a polynomial function divide the graph into intervals.