1. Adding and subtracting polynomials.
Multiplying and factoring.
What you’ll learn
To classify, add, and subtract polynomials.
To multiply a monomial by a polynomial.
To factor a monomial from a polynomial.
Vocabulary
Monomial, degree of a monomial, polynomial,
Standard form of a polynomial, binomial, trinomial.

2. Monomial: is a number, a variable, or a product
Take a note:
Monomial: is a number, a variable, or a product
of a number and one or more variables.
Degree of a monomial: is the sum of the exponents of
its variables.
Polynomial: is a monomial or the sum of monomials.
Degree of a polynomial: in one variable is the same as
the degree of the monomial with the greatest exponent.

3. xy a. c. d. b. Reason no yes yes yes
Determine whether each expression is a monomial. Explain your reasoning. xy d. c. b. a.
Reason
Monomial?
Expression
The expression involves subtraction, not the product, of two variables. no
yes
The expression is the product of a number and two variables.
is a real number and an example of a constant.
yes
yes
The expression is the product of two variables.

4. Determine whether each expression is a monomial. Explain your reasoning.b. a.
Reason
Monomial?
Expression
yes
Single variables are monomials. no
The expression involves subtraction, not the product, of two variables. no
The expression is the quotient, not the product, of two variables.
The expression is the product of a number, , and two variables.
yes
Example 1-1b

5. Find the degree of each monomial.
Degree of monomial
Monomial 3 4 8 3 2 1
Example 4-3a

6. Find the degree of each polynomial.b. a.
Degree of Polynomial
Degree of Each Term
Terms
Polynomial
0, 1, 2, 3 3
2, 1, 0 2 8 8
Example 4-3a

7. Monomial, Binomial, or Trinomial
State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial.
Monomial, Binomial, or Trinomial
Polynomial?
Expression a. b. c. d.
Yes
binomial
Yes
trinomial No
none of these
Yes
monomial
Example 4-1a

8. Monomial, Binomial, or Trinomial
State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial.
Monomial, Binomial, or Trinomial
Polynomial?
Expression a. b. c. d.
Yes
trinomial
No which is not a monomial.
none of these
Yes
binomial
Yes
monomial
Example 4-1b

9. Find the degree of each polynomial.b. a.
Degree of Polynomial
Degree of Each Term
Terms
Polynomial
2, 1, 3, 0 3
2, 4, 3 4
7, 6 7
Example 4-3b

10. Problem 1: Finding the degree of a monomial.
What is the degree of each monomial?
Degree
a)1
b)3+2=5
c)0
Degree
d)2
e)5
f)0
Answers
Problem 2: Adding and Subtracting Monomials
Answers
Just combine
like terms

11. Take a note: The standard form of a polynomial means
that the degrees of its monomials terms decrease
from left to right. You can name a polynomial by its
degree or by the number of monomials its contains.
Your turn:
Write each polynomial in standard form. What is the name
of the polynomial base on its degree and number of terms.
Answers

12. A D A L O V E L A C E

13. Problem 3:Multiplying a Monomial and a Trinomial
Use distributive property, applies properties of the exponents and simplify
Find
Example 6-1a

14. When expressions contain like terms, simplify by combining the like terms.
Simplify
Answer:
Example 6-2a

15. 
Simplify
Answer:
Example 6-2b

16. Problem 4: Finding the GCF
a)What is the GCF of
List the prime factor for all terms
Identify the factors common to all terms
Answer

17. Problem 5: Factoring Out a Monomial
What is the factored form of following polynomials.
Answers:

18. A helicopter landing pad, or helipad
Problem 6:
A helicopter landing pad, or helipad
is sometimes marked with a circle inside a square so
that is visible from the air. What is the area of the
shaded region of the helipad at the right? Write your
answer in factored form.
Find the area of the square region x
Find the area of the circle
To find area of the red area 2x
Factor the expression

19. 3x 6x Your turn Suppose the side length of the square is 6x and the
radius of the circle is 3x. What is the factored form
of the area of the shaded region? 3x 6x
Answer:

20. Classwork odd Homework even
TB pgs exercises 8-47
TB pgs exercises 9-41