Unit 2: Expressions and Polynomials

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Presentation transcript:

Unit 2: Expressions and Polynomials Closure Property and Polynomials

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.

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.

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.

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.

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 2. 4+2=6. Therefore the degree is six and it can be referred to as a sixth degree monomial.

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.

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.

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.

Put in Standard Form