math 71a 5.1 – introduction to polynomials and polynomial functions 1
TRANSCRIPT
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Math 71A
5.1 – Introduction to Polynomials and Polynomial Functions
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A number or a number multiplied by variables is called a ________________(also called a ________).
Polynomials
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A number or a number multiplied by variables is called a ________________(also called a ________).
Polynomials
monomial
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A number or a number multiplied by variables is called a ________________(also called a ________).
Polynomials
monomialterm
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Ex 1.Which of the following are monomials? 17
Polynomials
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Polynomials
Ex 1.Which of the following are monomials? 17
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The sum of the exponents of the variables is called the ________________ of a monomial.
The numerical factor in a monomial is called the ___________________.
Polynomials
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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
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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
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Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
17
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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
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Ex 2.What are the degrees and coefficients of the following monomials?
PolynomialsMonomial Degree Coefficient
2 -4
13 5
4 2
1
17
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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
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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
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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
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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
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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
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A polynomial with 2 terms is called a ____________________.
A polynomial with 3 terms is called a ____________________.
Polynomials
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A polynomial with 2 terms is called a ____________________.
A polynomial with 3 terms is called a ____________________.
Polynomials
binomial
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A polynomial with 2 terms is called a ____________________.
A polynomial with 3 terms is called a ____________________.
Polynomials
binomial
trinomial
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Ex 3.Add:
Adding Polynomials
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Ex 3.Add:
Adding Polynomials
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Ex 3.Add:
Adding Polynomials
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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
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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
smooth
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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
smooth
continuous
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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: ______
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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: ______
leading term
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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: ______
leading termhighest
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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: ______
leading termhighest
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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: ______
leading termhighest
𝟕 𝒙𝟔
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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: ______
leading termhighest
𝟕 𝒙𝟔 𝟕
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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: ______
leading termhighest
𝟕 𝒙𝟔 𝟕
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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: ______
leading termhighest
𝟕 𝒙𝟔 𝟕
−𝟑𝒙𝟒
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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: ______
leading termhighest
𝟕 𝒙𝟔 𝟕
−𝟑𝒙𝟒 −𝟑