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School
Florida International University *
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Course
1105L
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
2
Uploaded by ChancellorDanger13909
MAC1105L Topics Needed for Definitions of Polynomials and Sketching their Graphs
Worksheet 18
Name:____________________ Name:____________________
Name:____________________ Name:____________________
Name:____________________
In order to sketch a polynomial function you must recall first some previous topics. This worksheet is designed to help you remember how to solve polynomial equations and how to find the y-
intercept of a function.
Solving Polynomial Equations in Factored form
Example: Solve
−
2
x
(
x
+
5
)
2
(
x
−
3
)
=
0
Answer
:
recall the zero product property
x
=
0
,
∨
x
=−
5
,
∨
x
=
3
Solve:
1) 5
(
x
−
2
)
4
(
x
+
1
) (
x
−
5
)
=
0
2) x
3
(
x
−
1
)
3
(
x
−
3
)
2
=
0
Solving Polynomials Equations in Expanded Form
Example: Solve x
3
+
3
x
2
−
x
−
3
=
0
Answer
:
factor completely
x
=−
3
,
∨
x
=−
1
,
∨
x
=
1
Exercise: Factor and solve using the method of your choice
1) x
4
−
4
x
3
+
4
x
2
=
0
3) x
4
−
2
x
2
+
1
=
0
2) x
3
−
3
x
2
=
0
4) x
2
−
25
9
=
0
MAC1105L Topics Needed for Definitions of Polynomials and Sketching their Graphs
Worksheet 18
Finding the y-intercept
Example: Find the y-intercept of f
(
x
)
=
(
x
−
2
)
2
(
x
−
3
)
Answer
:
y-intercept is the axis where x=0
(
0
,
−
12
)
Exercise: Find the y-intercept of the following.
1) f
(
x
)
=
3
2
x
2
−
x
3
+
20
3) f
(
x
)
=−
2
x
3
(
x
−
1
)
2
(
x
+
5
)
2) f
(
x
)
=
6
x
3
−
9
x
−
x
5
4) f
(
x
)
=
(
x
+
3
) (
x
+
1
)
3
(
x
+
4
)
End Behavior and Multiplicity
To graph polynomial functions you will need to know some information about the polynomial such as the end behavior and multiplicity of roots.
Example: Find the end behavior and multiplicity of the roots given f
(
x
)
=
3
x
(
x
−
2
)
2
(
x
+
5
)
7
Answer
:
Leading Coefficient Test on 3
x
10
tells us the graph rises to positive infinity on the left and the right.
x
=
0
,multiplicity
1
x
=
2
,multiplicity
2
x
=−
5
,multiplicity
7
Exercise: Find the end behavior and multiplicity of the roots
1) f
(
x
)
=
5
(
x
−
2
)
4
(
x
+
1
) (
x
−
5
)
2) f
(
x
)
=
x
4
−
2
x
2
+
1
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