Lesson 4.10 - Multiplicity Learning Obiectives Students will be able to
1 Identify the multiplicity of a factor of a polynomial
2 Explore (and ultimately explain) the relationship between the factors of a
3 Describe how multiplicity affects the graph of a polynomial at its zeros
Making a connection
• In lesson 4.9, we learned the basic parts of polynomial graphs. This lesson is an
activity designed to explore the relationship between the factors of a polynomial, its
• Key Concept: Multiplicity - the number of times that a single "zero" or "solution" is
a root for a particular polynomial
> Example - if the factors of a polynomial are (x + 1)(x - 3)(x - 3) then the
solutions/zeros are -1 and 3 Since (x - 3) results in the same solution twice and
can also be written as (x - 3)". In this case, the factor is said to have a
"multiplicity of 2". This can also be referred to as a "double root since it yields
the same solution twice
Discovery Activity Part 1
Factor the following polynomial XP-21-4x+8
List the factors and their multiplicities in the chart below
Factor Multiplicity
Graph the polynomial using Desmos
List the coordinates of the x intercepts in the space below (these are the "zeros)
What is different about how the graph interacts with each zero? Does the graph pass
through the intercept or does the graph "bounce" off of the intercept at each zero?
What is different about the multiplicities of each factor?