1. Chapter 4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-1 Exponents and Polynomials

2. 2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-2 4.1 – Exponents 4.2 – Negative Exponents 4.3 – Scientific Notation 4.4 – Addition and Subtraction of Polynomials 4.5 – Multiplication of Polynomials 4.6 – Division of Polynomials Chapter Sections

3. 3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-3 Addition and Subtraction of Polynomials

4. 4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-4 Identifying Polynomials A polynomial in x is an expression that is the sum of a finite number of terms of the form ax n, for any real number a and any whole number n. Examples of Polynomials: a.) 8x b.) c.) Not Polynomials: a.) 4x 1/2 b.) 3x 2 + 4x -1 +5 c.) 4 +

5. 5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-5 Identifying Polynomials A polynomial is written in descending order when the exponents on the variable decrease from left to right. Example: 2x 4 + 4x 2 – 6x + 3 A polynomial with one term is called a monomial. A binomial is a two-termed polynomial. A trinomial is a three-termed polynomial.

6. 6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-6 Identifying Polynomials The degree of a term in one variable is the exponent on the variable in that term. The degree of 2x 3 is 3. The degree of a polynomial is the same as that of its highest-degree term. The degree of x 2 – 4 is 2, because x 2 is the highest-degree term The degree of a term in two or more variables is the sum of the exponents on the variables. The degree of 2x 2 y 3 is 5.

7. 7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-7 Adding Polynomials To add polynomials, combine the like terms of the polynomials. Example: a.)(4x 2 + 6x + 3) + (2x 2 + 5x - 1) = 4x 2 + 6x + 3+ 2x 2 + 5x - 1= 4x 2 + 2x 2 + 6x + 5x + 3 – 1 = 6x 2 + 11x + 2

8. 8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-8 Add Polynomials in Columns 1. Arrange polynomials in descending order, one under the other with like terms in the same columns. 2. Add the terms in each column. Example: Add 5x 2 – 9x – 3 and -3x 2 – 4x + 6 using columns. 5x 2 – 9x – 3 -3x 2 – 4x + 6 2x 2 – 13x + 3

9. 9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-9 Subtracting Polynomials 1.Use the distributive property to remove parentheses. This will have the effect of changing the sign of every term within the parentheses of the polynomial being subtracted. –(4x 3 + 5x 2 – 8) = – 4x 3 – 5x 2 + 8 2.Combine like terms. Example: (3x 2 – 2x + 5) – (x 2 – 3x + 4) = 3x 2 – 2x + 5 – x 2 + 3x – 4 = 2x2 + x + 1

10. 10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-10 Subtract Polynomials in Columns 1. Write the polynomial being subtracted below the polynomial from which it is being subtracted. List the terms in the same column. 2. Change the sign of each term in the polynomial being subtracted. 3. Add the terms in each column.

11. 11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-11 Subtract Polynomials in Columns Example: Subtract 2x 2 – 4x + 6 and 4x 2 + 5x + 8 using columns. 4x 2 + 5x + 8 -2x 2 + 4x – 6 2x 2 + 9x + 2 Changed all signs