CHAPTER 3
3-1 polynomials
SAT Problem of the day
• What is the distance between the origin and the point
(-5,9)?
• A)5.9
• B)6.7
• C)8.1
• D)10.3
• E)11.4
Solution to the SAT Problem
• Right Answer: D)
Objectives
Identify, evaluate, add, and subtract polynomials.
Classify and graph polynomials.
Polynomials
• What is a monomial?
• A monomial is a number or a product of numbers and
variables with whole number exponents.
• What is a polynomial?
• polynomial is a monomial or a sum or difference of
monomials. Each monomial in a polynomial is a term.
Because a monomial has only one term, it is the simplest
type of polynomial.
Polynomial examples
• Polynomials have no variables in denominators or
exponents, no roots or absolute values of variables, and
all variables have whole number exponents.
• Polynomials:
• Not polynomials:
Degree of a polynomial
• The degree of a monomial is the sum of the exponents
of the variables.
Example#1
• Identify the degree of each monomial.
• A. z6
• B. 5.6
• C. 8xy3
• D. a2bc3
Student guided practice
Degree of a polynomial
• An degree of a polynomial is given by the term with the
greatest degree. A polynomial with one variable is in
standard form when its terms are written in descending
order by degree. So, in standard form, the degree of the
first term indicates the degree of the polynomial, and the
leading coefficient is the coefficient of the first term.
Polynomial classification
• A polynomial can be classified by its number of terms. A
polynomial with two terms is called a binomial, and a
polynomial with three terms is called a trinomial. A
polynomial can also be classified by its degree.
Example#2
• Rewrite each polynomial in standard form. Then
identify the leading coefficient, degree, and number of
terms. Name the polynomial.
• A. 3 – 5x2 + 4x
• B. 3x2 – 4 + 8x4
Student guided practice
Adding and subtracting polynomials
• To add or subtract polynomials, combine like terms. You
can add or subtract horizontally or vertically
Example#3
• Add or subtract. Write your answer in standard form.
• A. (2x3 + 9 – x) + (5x2 + 4 + 7x + x3
Example#4
• Add or subtract. Write your answer in standard form.
• B. (3 – 2x2) – (x2 + 6 – x)
Example#5
• Add or subtract. Write your answer in standard form
• (–36x2 + 6x – 11) + (6x2 + 16x3 – 5)
Student guided practice
• Do problems 10-17 from your book page 154
homework
• Do problems 19-30 from your book page 154
closure
Today we learned about polynomials and how we add
them.
Next class we are going to learned about how we can
multiply polynomials