1. Unit 2: Expressions and Polynomials
Closure Property and Polynomials

2. Closure Property With a partner:
Using the numbers {-1, 0, 1}, take turns choosing 2 numbers at a time and multiplying them together.
If the answer is -1, 0, or 1, you score a point.
Play 4 turns each
Did either of you win?
Play again, but this time use subtraction.

3. Closure Property
When you perform an operation on any two numbers in a set and produce a number in the set, the set is closed under that operation.
The set {-1, 0, 1} is closed under multiplication, but not under subtraction.

4. Vocabulary
Monomial: A number, a variable or the product of a number and one or more variables
Polynomial: A monomial or a sum of monomials.
Binomial: A polynomial with exactly two terms.
Trinomial: A polynomial with exactly three terms.
Coefficient: A numerical factor in a term of an algebraic expression.
Degree of a monomial: The sum of the exponents of all of the variables in the monomial.

5. Vocabulary
Degree of a polynomial in one variable: The largest exponent of that variable.
Standard form: When the terms of a polynomial are arranged from the largest exponent to the smallest exponent in decreasing order.

6. Degree of a Monomial What is the degree of the monomial?
The degree of a monomial is the sum of the exponents of the variables in the monomial.
The exponents of each variable are 4 and =6.
Therefore the degree is six and it can be referred to as a sixth degree monomial.

7. Polynomial The number factor of a term is called the coefficient.
A polynomial is a monomial or the sum of monomials
Each monomial in a polynomial is a term of the polynomial.
The number factor of a term is called the coefficient.
The coefficient of the first term in a polynomial is the lead coefficient
A polynomial with two terms is called a binomial.
A polynomial with three terms is called a trinomial.

8. Degree of a Polynomial in One Variable
The degree of a polynomial in one variable is the largest exponent of that variable.
The degree of this polynomial is 2, since the highest exponent of the variable x is 2.

9. Standard Form of a Polynomial
To rewrite a polynomial in standard form, rearrange the terms of the polynomial starting with the largest degree term and ending with the lowest degree term.

10. Put in Standard Form