Introduction To Polynomials

The following are examples of monomials in one variable

The following are examples of monomials in one variable

The following are examples of monomials in one variable

The following are examples of monomials in one variable

The following are examples of monomials in one variable

The following are examples of monomials in one variable

A monomial is an expression of the type axn,

A monomial is an expression of the type axn, where a is a real number constant

A monomial is an expression of the type axn, where a is a real number constant and n is a nonnegative integer.

Algebraic expressions like the following are polynomials.

Algebraic expressions like the following are polynomials.

Algebraic expressions like the following are polynomials.

Algebraic expressions like the following are polynomials.

Algebraic expressions like the following are polynomials.

Algebraic expressions like the following are polynomials.

Algebraic expressions like the following are polynomials.

Algebraic expressions like the following are polynomials.

Algebraic expressions like the following are polynomials.

Algebraic expressions like the following are polynomials.

A polynomial is a monomial or a combination of sums and/or differences of monomials.

The following algebraic expressions are not polynomials.

The following algebraic expressions are not polynomials.

The following algebraic expressions are not polynomials.

The following algebraic expressions are not polynomials.

The following algebraic expressions are not polynomials. Polynomials do not contain quotients.

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = 2

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

Evaluate the polynomial when x = -4

x Use only the given graph of y = 2x – 2 to evaluate the polynomial

x Use only the given graph of y = 2x – 2 to evaluate the polynomial when x = 3 x

x Use only the given graph of y = 2x – 2 to evaluate the polynomial when x = 3 x

x Use only the given graph of y = 2x – 2 to evaluate the polynomial when x = 3 x

x Use only the given graph of y = 2x – 2 to evaluate the polynomial when x = 3 x

x Use only the given graph of y = 2x – 2 to evaluate the polynomial when x = 3 x

x Use only the given graph of y = 2x – 2 to evaluate the polynomial when x = 3 x

In a sports league of x teams in which each team plays every other team twice, the total number of games N to be played is given by the polynomial equation

In a sports league of x teams in which each team plays every other team twice, the total number of games N to be played is given by the polynomial equation N = x2 – x

In a sports league of x teams in which each team plays every other team twice, the total number of games N to be played is given by the polynomial equation N = x2 – x A women’s slow-pitch softball league has 10 teams.

In a sports league of x teams in which each team plays every other team twice, the total number of games N to be played is given by the polynomial equation N = x2 – x A women’s slow-pitch softball league has 10 teams. What is the total number of games to be played?

Evaluate the polynomial when x = 10

Evaluate the polynomial when x = 10

Evaluate the polynomial when x = 10

Evaluate the polynomial when x = 10

Evaluate the polynomial when x = 10

Evaluate the polynomial when x = 10

Evaluate the polynomial when x = 10

Evaluate the polynomial when x = 10

Evaluate the polynomial when x = 10

Evaluate the polynomial when x = 10

The concentration C, in parts per million of a certain antibiotic in the bloodstream after t hours is given by the polynomial expression

The concentration C, in parts per million of a certain antibiotic in the bloodstream after t hours is given by the polynomial expression C = -0.05t2 + 2t + 2

The concentration C, in parts per million of a certain antibiotic in the bloodstream after t hours is given by the polynomial expression C = -0.05t2 + 2t + 2 To find the concentration after 2 hours, we evaluate the polynomial when t = 2

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 0

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 2

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 10

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 20

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

Evaluate the polynomial when t = 30

The polynomial in the previous example can be graphed if we evaluate the polynomial for several values of t. We list the values in a table and show the graph below.

The concentration peaks when x = 20. After 40 hours the concentration is 0.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Find an equivalent polynomial using only addition.

Identify the terms of the polynomial

Identify the terms of the polynomial

Identify the terms of the polynomial

Identify the terms of the polynomial

Identify the terms of the polynomial

Identify the terms of the polynomial

Identify the terms of the polynomial

Identify the terms of the polynomial

Identify the terms of the polynomial

Identify the terms of the polynomial

Identify the terms of the polynomial

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

When you add like terms you get like terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Like Terms Not Like Terms

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Identify the like terms of the polynomial

Coefficients What is the coefficient of the term?

Coefficients What is the coefficient of the term?

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Coefficients Identify the coefficients

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Collect the like terms.

Descending order

Descending order

Descending order

Descending order

Descending order

Descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

Collect like terms and arrange the polynomial in descending order

The degree of a term is the exponent of the variable.

The degree of a term is the exponent of the variable. What is the degree of the term?

The degree of a term is the exponent of the variable. What is the degree of the term?

The degree of a term is the exponent of the variable. What is the degree of the term?

Identify the degree of each term of

Identify the degree of each term of

Identify the degree of each term of

Identify the degree of each term of

Identify the degree of each term of

Identify the degree of each term of

Identify the degree of each term of

Identify the degree of each term of

The degree of a polynomial is the largest of the degrees of the terms, unless it is the polynomial 0.

The polynomial 0 is a special case.

The polynomial 0 is a special case.

The polynomial 0 is a special case. We agree that it has no degree either as a term or as a polynomial.

The polynomial 0 is a special case. We agree that it has no degree either as a term or as a polynomial. This is because we can express

The polynomial 0 is a special case. We agree that it has no degree either as a term or as a polynomial. This is because we can express 0 as 0x5 = 0x7,

The polynomial 0 is a special case. We agree that it has no degree either as a term or as a polynomial. This is because we can express 0 as 0x5 = 0x7, and so on, using any exponent we wish.

Identify the degree of the polynomial

Identify the degree of the polynomial

Identify the degree of the polynomial

Identify the degree of the polynomial

Identify the degree of the polynomial

Identify the degree of the polynomial

Identify the degree of the polynomial

Identify the degree of the polynomial

Identify the degree of the polynomial

Lets summarize the terminology that we have learned Lets summarize the terminology that we have learned. Using the polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Term Coefficient Degree of the Term Degree of the Polynomial

Missing terms. Identify the missing terms in the polynomial

Missing terms. Identify the missing terms in the polynomial

Missing terms. Identify the missing terms in the polynomial

Missing terms. Identify the missing terms in the polynomial

Missing terms. Identify the missing terms in the polynomial

Missing terms. Identify the missing terms in the polynomial

Missing terms. Identify the missing terms in the polynomial

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Missing terms. Write the polynomial with its missing terms

Classifying Polynomials

Classifying Polynomials Polynomials with one term are called monomials.

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials.

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials.

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Classifying Polynomials Polynomials with one term are called monomials. Polynomials with two terms are called binomials. Polynomials with three terms are called trinomials. MONOMIALS BINOMIALS TRINOMIALS NONE OF THESE

Lesson 4.3 Numbers 1 - 100