Polynomials

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Slide 1

Polynomials

Slide 2

Objectives

Be able to determine the degree of a polynomial.

Be able to classify a polynomial.

Be able to write a polynomial in standard form.

Slide 3

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.

Slide 4

Vocabulary

Degree of a monomial: The sum of the exponents of all of the variables in the monomial.

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.

Slide 5

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.

The degree of the monomial is 6.

The monomial can be referred to as a sixth degree monomial.

Slide 6

Polynomials in One Variable

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.

Slide 7

Polynomials in One Variable

The degree of a polynomial in one variable is the largest exponent of that variable.

A constant has no variable. It is a 0 degree polynomial.

This is a 1st degree polynomial. 1st degree polynomials are linear.

This is a 2nd degree polynomial. 2nd degree polynomials are quadratic.

This is a 3rd degree polynomial. 3rd degree polynomials are cubic.

Slide 8

Classify the polynomials by degree and number of terms.

Example

Polynomial

a.

b.

c.

d.

Degree

Classify by degree

Classify by number of terms

Zero

Constant

Monomial