Polynomials: Multiplicity
Presentation
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Easy
Standards-aligned
Tia Rebecca
Used 6+ times
FREE Resource
4 Slides • 10 Questions
1
PSA: READ the slides
2
VOCABULARY: Multiplicity
Multiplicity refers to the number of times a root occurs.
Example: y = (x - 3)(x + 7)2(x - 5)3
x = 3 has a multiplicity of 1
x = -7 has a multiplicity of 2
x = 5 has a multiplicity of 3
3
Multiple Choice
What does multiplicity mean?
The number of times a zero occurs.
The number of factors being multiplied.
The degree of a polynomial.
4
Dropdown
f(x) = x4 (x - 9)3 (x + 12)
x = 0 has a multiplicity of
x = 9 has a multiplicity of
x = -12 has a multiplicity of
5
Dropdown
f(x) = x2 -2x - 24
Hint: Factor f(x) first.
(smallest number) x =
(largest number) x =
6
Multiple Choice
Imagine the graph of g(x) = (x - 5)2
What happens at x = 5?
The graph "bounces" off of the x-axis, creating a minimum/maximum at that zero.
The graph crosses through the x-axis.
7
Multiple Choice
Imagine the graph of k(x) = -x - 4.
What happens at x = -4?
The graph "bounces" off of the x-axis, creating a minimum/maximum at that zero.
The graph crosses through the x-axis.
8
Multiple Choice
Use your graphing calculator to graph
f(x) = (x - 3)2 (x + 4)5
What happens at x = 3?
The graph "bounces" off of the x-axis, creating a minimum/maximum at that zero.
The graph crosses through the x-axis.
9
Multiple Choice
Use your graphing calculator to graph
f(x) = (x - 3)2 (x + 4)5
What happens at x = -4?
The graph "bounces" off of the x-axis, creating a minimum/maximum at that zero.
The graph crosses through the x-axis.
10
On the next slide, observe the patterns in behavior when multiplicity is even and odd.
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12
Match
Without a calculator, match the polynomial with its graph.
f(x)= x3-3x2
f(x)= -2x3+8x
f(x)= -x3+9x
f(x)= 3x4-3x3-3x2+3x
f(x)= -2x2+16x-24
f(x)= x3-3x2
f(x)= -2x3+8x
f(x)= -x3+9x
f(x)= 3x4-3x3-3x2+3x
f(x)= -2x2+16x-24
13
Match
Without a calculator, match the polynomial with its graph.
f(x)=-3(x-1)(x-2)2(x-3)
f(x)=(x-1)(x-3)(x-5)
f(x)= -(x-4)(x-3)(x-1)2
f(x)=-5
f(x)=x
f(x)=-3(x-1)(x-2)2(x-3)
f(x)=(x-1)(x-3)(x-5)
f(x)= -(x-4)(x-3)(x-1)2
f(x)=-5
f(x)=x
14
Match
Without a calculator, match the polynomial with its graph.
f(x)= 9-4x2
f(x)= x2(x-3)3
f(x)= x4-3x3
f(x)= -2(x+3)2(x+1)2
f(x)= x4-6x3+8x2
f(x)= 9-4x2
f(x)= x2(x-3)3
f(x)= x4-3x3
f(x)= -2(x+3)2(x+1)2
f(x)= x4-6x3+8x2
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