Math 71A 5.1 – Introduction to Polynomials and Polynomial Functions 1.
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Transcript of Math 71A 5.1 – Introduction to Polynomials and Polynomial Functions 1.
1
Math 71A
5.1 – Introduction to Polynomials and Polynomial Functions
2
A number or a number multiplied by variables is called a ________________(also called a ________).
Polynomials
3
A number or a number multiplied by variables is called a ________________(also called a ________).
Polynomials
monomial
4
A number or a number multiplied by variables is called a ________________(also called a ________).
Polynomials
monomialterm
5
Ex 1.Which of the following are monomials? 17
Polynomials
6
Polynomials
Ex 1.Which of the following are monomials? 17
7
The sum of the exponents of the variables is called the ________________ of a monomial.
The numerical factor in a monomial is called the ___________________.
Polynomials
8
The sum of the exponents of the variables is called the ________________ of a monomial.
The numerical factor in a monomial is called the ___________________.
Polynomials
degree
9
The sum of the exponents of the variables is called the ________________ of a monomial.
The numerical factor in a monomial is called the ___________________.
Polynomials
degree
coefficient
10
Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
17
11
Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
2 -4
17
12
Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
2 -4
13 5
17
13
Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
2 -4
13 5
4 2
17
14
Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
2 -4
13 5
4 2
1
17
15
Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
2 -4
13 5
4 2
1
2 1
17
16
Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
2 -4
13 5
4 2
1
2 1
1 -1
17
17
Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
2 -4
13 5
4 2
1
2 1
1 -1
17 0 17
18
One or more monomials added together is called a ___________________.
ex:
The highest degree of all terms in a polynomial is called the _________________ of the polynomial.
ex: What is degree of above polynomial?
Polynomials
19
One or more monomials added together is called a ___________________.
ex:
The highest degree of all terms in a polynomial is called the _________________ of the polynomial.
ex: What is degree of above polynomial?
Polynomials
polynomial
20
One or more monomials added together is called a ___________________.
ex:
The highest degree of all terms in a polynomial is called the _________________ of the polynomial.
ex: What is degree of above polynomial?
Polynomials
polynomial
degree
21
One or more monomials added together is called a ___________________.
ex:
The highest degree of all terms in a polynomial is called the _________________ of the polynomial.
ex: What is degree of above polynomial?
Polynomials
polynomial
degree
2+3=𝟓
22
A polynomial with 2 terms is called a ____________________.
A polynomial with 3 terms is called a ____________________.
Polynomials
23
A polynomial with 2 terms is called a ____________________.
A polynomial with 3 terms is called a ____________________.
Polynomials
binomial
24
A polynomial with 2 terms is called a ____________________.
A polynomial with 3 terms is called a ____________________.
Polynomials
binomial
trinomial
25
Ex 3.Add:
Adding Polynomials
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Ex 3.Add:
Adding Polynomials
27
Ex 3.Add:
Adding Polynomials
28
Ex 4.Subtract:
Subtracting Polynomials
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Ex 4.Subtract:
Subtracting Polynomials
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Ex 4.Subtract:
Subtracting Polynomials
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Here’s a polynomial function: And here’s what looks like:
Polynomial Functions
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In general, polynomial functions are __________ (i.e.
only have rounded curves with no sharp corners) and
________________ (i.e. don’t have breaks and can be
drawn without lifting pencil).
Polynomial Functions
33
In general, polynomial functions are __________ (i.e.
only have rounded curves with no sharp corners) and
________________ (i.e. don’t have breaks and can be
drawn without lifting pencil).
Polynomial Functions
smooth
34
In general, polynomial functions are __________ (i.e.
only have rounded curves with no sharp corners) and
________________ (i.e. don’t have breaks and can be
drawn without lifting pencil).
Polynomial Functions
smooth
continuous
35
Also, polynomial functions always either rise or fall as you go to the left or right (except for constant functions).
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This is called the end behavior of a function, and depends on the ______________ (the term with _________ degree).
Ex 5.Find the leading term and leading coefficient of the following polynomial functions. Leading term: ______ Leading coefficient: ______ Leading term: ______ Leading coefficient: ______
37
This is called the end behavior of a function, and depends on the ______________ (the term with _________ degree).
Ex 5.Find the leading term and leading coefficient of the following polynomial functions. Leading term: ______ Leading coefficient: ______ Leading term: ______ Leading coefficient: ______
leading term
38
This is called the end behavior of a function, and depends on the ______________ (the term with _________ degree).
Ex 5.Find the leading term and leading coefficient of the following polynomial functions. Leading term: ______ Leading coefficient: ______ Leading term: ______ Leading coefficient: ______
leading termhighest
39
This is called the end behavior of a function, and depends on the ______________ (the term with _________ degree).
Ex 5.Find the leading term and leading coefficient of the following polynomial functions. Leading term: ______ Leading coefficient: ______ Leading term: ______ Leading coefficient: ______
leading termhighest
40
This is called the end behavior of a function, and depends on the ______________ (the term with _________ degree).
Ex 5.Find the leading term and leading coefficient of the following polynomial functions. Leading term: ______ Leading coefficient: ______ Leading term: ______ Leading coefficient: ______
leading termhighest
𝟕 𝒙𝟔
41
This is called the end behavior of a function, and depends on the ______________ (the term with _________ degree).
Ex 5.Find the leading term and leading coefficient of the following polynomial functions. Leading term: ______ Leading coefficient: ______ Leading term: ______ Leading coefficient: ______
leading termhighest
𝟕 𝒙𝟔 𝟕
42
This is called the end behavior of a function, and depends on the ______________ (the term with _________ degree).
Ex 5.Find the leading term and leading coefficient of the following polynomial functions. Leading term: ______ Leading coefficient: ______ Leading term: ______ Leading coefficient: ______
leading termhighest
𝟕 𝒙𝟔 𝟕
43
This is called the end behavior of a function, and depends on the ______________ (the term with _________ degree).
Ex 5.Find the leading term and leading coefficient of the following polynomial functions. Leading term: ______ Leading coefficient: ______ Leading term: ______ Leading coefficient: ______
leading termhighest
𝟕 𝒙𝟔 𝟕
−𝟑𝒙𝟒
44
This is called the end behavior of a function, and depends on the ______________ (the term with _________ degree).
Ex 5.Find the leading term and leading coefficient of the following polynomial functions. Leading term: ______ Leading coefficient: ______ Leading term: ______ Leading coefficient: ______
leading termhighest
𝟕 𝒙𝟔 𝟕
−𝟑𝒙𝟒 −𝟑