1. Objectives Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Expressions and Polynomials 1. Differentiate between an expression and an equation. 2. Evaluate expressions. 3.1

2. 3.1 - 2 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 1 Differentiate between an expression and an equation.

3. 3.1 - 3 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definition Equation: A mathematical relationship that contains an equal sign. These are equations…they contain an equal sign (=). P = 2l + 2w V= lwh These are expressions…they do not contain an equal sign. 2l + 2w lwh

4. 3.1 - 4 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definition Expression: A constant, variable, or any combination of constants, variables, and arithmetic symbols that describes a calculation. N = R − C is an equation, whereas R − C is an expression. 4 + 7 = 11 is an equation, whereas 4 + 7 is an expression. V = lwh is an equation, whereas lwh is an expression.

5. 3.1 - 5 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 1 Determine whether each of the following is an expression or an equation and explain why. a. 16 5 = 80 b. d = rt c. 4x + 7

6. 3.1 - 6 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 2 Evaluate expressions.

7. 3.1 - 7 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley There are two actions we can perform with an expression.  Evaluate.  Rewrite. In this section, we will focus on evaluating expressions…

8. 3.1 - 8 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To evaluate an expression. Procedure 1.Replace the variable with the corresponding given values. 2.Calculate using the order of operations agreement.

9. 3.1 - 9 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 2 Evaluate: x 2 + 5xy − 7 when x = – 3 and y = 2

10. 3.1 - 10 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 3 Evaluate – x + 5(x + y) when x = – 3 and y = 1

11. 3.1 - 11 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 4 Evaluate │r 2 − p│+ 4r when r = – 2 and p = 6

12. 3.1 - 12 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 5 Evaluate: when m = – 6 and n = 2.

13. 3.1 - 13 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 6 Evaluate when h = 2 and k = – 5.

14. 3.1 - 14 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Division Properties If the divisor is 0 and the dividend is any number other than 0, the quotient is undefined. n ÷ 0, or, is undefined, when n ≠ 0. When 0 is divided by any number other than 0, the quotient is 0. 0 ÷ n = = 0, when n ≠ 0. If the dividend and divisor are both 0, the quotient is indeterminate. 0 ÷ 0, or is indeterminate. In math language:

15. 3.1 - 15 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 7 Find all values for the variable that cause to be undefined or indeterminate.