Objectives Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions.

A monomial is numbers or letters all multiplying (there are no + or – signs) The degree of a monomial is all the exponents added up. *If there is just a number, the degree is 0

Example 1: Finding the Degree of a Monomial Find the degree of each monomial. A. 4p4q3 The degree is 7. Add the exponents of the variables: 4 + 3 = 7. B. 7ed The degree is 2. Add the exponents of the variables: 1+ 1 = 2. C. 3 The degree is 0. Add the exponents of the variables: 0 = 0.

Check It Out! Example 1 Find the degree of each monomial. a. 1.5k2m The degree is 3. Add the exponents of the variables: 2 + 1 = 3. b. 4x The degree is 1. Add the exponents of the variables: 1 = 1. c. 2c3 The degree is 3. Add the exponents of the variables: 3 = 3.

A polynomial is a bunch of monomials with + or – signs. The degree of a polynomial is the degree of the monomial with the biggest degree.

Example 2: Finding the Degree of a Polynomial Find the degree of each polynomial. A. 11x7 + 3x3 11x7: degree 7 3x3: degree 3 Find the degree of each term. The degree of the polynomial is the greatest degree, 7. B. :degree 3 :degree 4 –5: degree 0 Find the degree of each term. The degree of the polynomial is the greatest degree, 4.

Check It Out! Example 2 Find the degree of each polynomial. a. 5x – 6 5x: degree 1 –6: degree 0 Find the degree of each term. The degree of the polynomial is the greatest degree, 1. b. x3y2 + x2y3 – x4 + 2 Find the degree of each term. x3y2: degree 5 x2y3: degree 5 –x4: degree 4 2: degree 0 The degree of the polynomial is the greatest degree, 5.

Standard Form Putting all the monomials in order of their degrees from biggest to smallest Leading Coefficient Th number in front of the first letter when written in standard form

Example 3A: Writing Polynomials in Standard Form Write the polynomial in standard form. Then give the leading coefficient. 6x – 7x5 + 4x2 + 9 Find the degree of each term. Then arrange them in descending order: 6x – 7x5 + 4x2 + 9 –7x5 + 4x2 + 6x + 9 Degree 1 5 2 –7x5 + 4x2 + 6x + 9. The standard form is The leading coefficient is –7.

Example 3B: Writing Polynomials in Standard Form Write the polynomial in standard form. Then give the leading coefficient. y2 + y6 − 3y Find the degree of each term. Then arrange them in descending order: y2 + y6 – 3y y6 + y2 – 3y Degree 2 6 1 The standard form is The leading coefficient is 1. y6 + y2 – 3y.

Check It Out! Example 3a Write the polynomial in standard form. Then give the leading coefficient. 16 – 4x2 + x5 + 9x3 Find the degree of each term. Then arrange them in descending order: 16 – 4x2 + x5 + 9x3 x5 + 9x3 – 4x2 + 16 Degree 2 5 3 The standard form is The leading coefficient is 1. x5 + 9x3 – 4x2 + 16.

Some polynomials have special names based on their degree and the number of terms they have. Monomial Binomial Trinomial Polynomial 4 or more 1 2 3 1 2 Constant Linear Quadratic 3 4 5 6 or more 6th,7th,degree and so on Cubic Quartic Quintic

Example 4: Classifying Polynomials Classify each polynomial according to its degree and number of terms. A. 5n3 + 4n 5n3 + 4n is a cubic binomial. Degree 3 Terms 2 B. 4y6 – 5y3 + 2y – 9 4y6 – 5y3 + 2y – 9 is a 6th-degree polynomial. Degree 6 Terms 4 C. –2x –2x is a linear monomial. Degree 1 Terms 1

Check It Out! Example 4 Classify each polynomial according to its degree and number of terms. a. x3 + x2 – x + 2 x3 + x2 – x + 2 is a cubic polynomial. Degree 3 Terms 4 b. 6 6 is a constant monomial. Degree 0 Terms 1 –3y4 + 18y3 + 14y is an Quartic trinomial. c. –3y4 + 18y3 + 14y Degree 4 Terms 3