Polynomials• Identify Monomials and their

Degree

• Identify Polynomials and their Degree

• Adding, Subtracting, Multiplying, and Dividing Polynomial Expressions

A monomial is the product of a constant times a variable

raised to a nonnegative integer power. The degree of a monomial is

the sum of the exponents of the variables. A polynomial is a monomial or

the sum of monomials.

The degree of a polynomial is the monomial with the highest

degree.

Polynomials cannot have the following:

1. Variables with negative exponents

2. Variable exponents

3. Variables under the radical sign

State the coefficient and the degree of each polynomial

5 41. 14a bc

7 4 2 82. 7a b 2a b

6 4 3 53. x 2x y 4y

1.Change (-) to (+) of the opposite

2.Use the Distributive Property3.Combine all like terms4.Write your answer in

standard form

Adding and SubtractingPolynomials

Simplify Each Expression

Multiplying Polynomials

1. Follow all rules for exponents2. FOIL Method for multiplying

binomials3. Use Distributive Property for all

others4. Use special products when

applicable5. Combine all like terms6. Write your answer in standard

form

Rule:1.Square2.2x the product3.Square

2 2 2

2 2 2

1

Perfect

. a b a 2ab b

2. a b a 2ab b

Square Trinomials

Squaring A Trinomial Square each term and 2x each

product

2 2

Difference of 2 Squ

a b a

are

b b

s

a

3 3 2 2 3

3 3 2 2 3

a b a 3

a b 3a

Cubing A Bin

b b

a b a 3a b 3ab b

omial

Perform the indicated operation below and express as a single

polynomial 1. x 2y x 2y

2. 4a 3b 4a 3b

3. 5x 4 y 5x 4 y

24. 5x 2 2

5. 4a 9b

Perform the indicated operation below and express as a single

polynomial 226. 4x y 5z 2

24 27. 5a 9b 4c

38. 2x 3 3

9. 4x 5

Perform the indicated operation below and express as a single

polynomial

Monomial Division

1. Divide each term by the Monomial

2. Follow your rules for exponents

Polynomial Division1. List all of the terms with their

powers in descending order

2. Replace any missing terms with a zero

3. Divide the polynomial until the degree of the divisor is greater than the degree of the remainder

4. Write the remainder over the divisor

Perform the indicated operation below

Synthetic Division

1. List all of the terms with their powers in descending order

2. Replace missing terms with a coefficient of 0

3. List all of the coefficients in descending order

4. Set the divisor equal to zero and solve

5. Write your final answer using the coefficients as one power less than the original polynomial

6. Write the remainder over the divisor

Perform the indicated operation below