Lesson 8 Add Subt Polynomials.notebook
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1 Lesson 8 Adding and Subtracting Polynomials Students understand that the sum or difference of two polynomials produces another polynomial and relate polynomials to the system of integers; students add and subtract polynomials. Classwork Exercise 1 (7 minutes) Have students complete Exercise 1 a) and use it for a brief discussion on the notion of base. Then have the students continue with the remainder of the exercise.
2 Pull
3 Teacher notes Pull Exercise 2 (5 minutes) Work through Exercise 2 with the class. Point out that the expression we see here is just the generalized form of their answer from b) of Exercise 1. But, as we change different number each time. x, we get a Exercise 3 (10 minutes) Allow students time to complete Exercise 3 individually. Then elicit responses from the class.
4 Discussion (11 minutes) The next item in your student materials is a definition for a polynomial expression. Read the definition carefully, and then create 3 polynomial expressions using the given definition. Note! Subtraction, division, and exponents are included in this definition Pull Compare your polynomial expressions with a neighbor. Do your neighbor s expressions fall into the category of a polynomial expression? List several of the student generated polynomials on the board, include some that contain more than one variable. Review from lesson 7
5 Discuss Create a monomial and compare with your neighbor Give an example of a polynomial based on the definitions.
6 A polynomial is in STANDARD form when its terms are arranged so that the exponents decrease in value from left to right. 3x +6 7x 5 +4x 2 Monomials 3x 2 ab 7s 2 t 5 Binomials a + b 2x x 2 y 2 Trinomials 2x 2 + 3x b + b 2
7 To find the degree : Rules: The degree of a monomial is the SUM of the exponents of the variables: 4x 3 has a degree of? 5cd 2 = degree of? The degree of a Polynomial is the greatest of the degrees of its monomials: 3x 7 + 4x 3 y 2 5x 4 Greatest is Monomial Degree The sum of the exponents of the variables in the term. 2x 3 y 2 Polynomial The degree of the monomial term with the highest degree. x 2-2x + 4
8 Definitions A binomial is the sum (or difference) of two monomials. A trinomial is the sum (or difference) of three monomials. A polynomial, as stated earlier, is the sum of one or more monomials. The degree of a monomial is the sum of the exponents of the variable symbols that appear in the monomial. The degree of a polynomial is the degree of the monomial term with the highest degree. While polynomials can contain multiple variable symbols, most of our work with polynomials will be with polynomials in one variable. What do polynomial expressions in one variable look like? Create a polynomial expression in one variable, and compare with your neighbor. Post some of the student generated polynomials in one variable on the board. In Standard Form: 4x 5 + 3x 2 6x + 1 What is a constant term of a polynomial?
9 Like Terms Two or more terms are considered like terms if they are identical. Only their numerical coefficients are different. 2x and 3x xy and 4xy 3x 2 and 2x 2 3m 3 n 2 and 5n 2 m 3 Are 6s 2 t 4 and 8s 4 t 2 like terms?
10 Exercise 4 (5 minutes)
11 Problem Set
12
13
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