Chapter 4.pdf - CHAPTER 4 Exponents and Polynomials Source Elementary Intermediate Algebra Fourth Edition Prepared and Edited by Dr Mohamad Hammoudi

# Chapter 4.pdf - CHAPTER 4 Exponents and Polynomials Source...

This preview shows page 1 - 13 out of 51 pages.

CHAPTER 4 Exponents and Polynomials Source: Elementary & Intermediate Algebra, Fourth Edition Prepared and Edited by: Dr. Mohamad Hammoudi
Topics of Chapter 4 4.1: Positive Integer Exponents. 4.2: Zero and Negative Exponents and Scientific Notation. 4.3: Introduction to Polynomials. 4.4: Addition and Subtraction of Polynomials. 4.5: Multiplication of Polynomials and Special Products. 4.6: Division of Polynomials. 2
4.1: Positive Integer Exponents Objectives: 4.1.1: Use exponential notation 4.1.2: Simplify expressions with positive integer exponents 3
Exponents Instead of writing 2 . 2 . 2 . 2 . 2 . 2 . 2, we may write 2 7 Instead of writing a . a . a . a . a, we may write a 5 We call ( a ) the base on the expression and ( 5 ) the exponent , or power . a 5 is read as “ a to the fifth power.” Definition of Exponential Expression: An expression of this type is said to be in exponential form . 4
4.1.1: Use Exponential Notation Examples: Write each of the following, using exponential notation. 1. 3 . 3 . 3 . 3 . 3 2. 5y . 5y . 5y 3. w . w . w . w 5
Product Rule for Exponents Let’s consider what happens when we multiply two expressions in exponential form with the same base . Notice that the product is simply the base taken to the power that is the sum of the two original exponents. 6
4.1.2: Simplify Expressions with Positive Integer Exponents Examples: Simplify each expression. 1. b 4 . b 6 2. (2a) 3 . (2a) 4 3. ( 2) 5 . ( 2) 2 4. (10 7 ) . (10 11 ) 7
4.1.2: Simplify Expressions with Positive Integer Exponents Using the product rule for exponents together with the commutative and associative properties, simplify each expression. Multiply the coefficients and add the exponents by the product rule. Examples: Using the product rule for exponents together with the commutative and associative properties, simplify each expression. 1. (x 4 ) (x 2 ) (x 3 ) (x) 2. (3x 4 ) (5x 2 ) 3. (2x 5 y) (9x 3 y 4 ) 4. ( 3x 2 y 2 ) ( 2x 4 y 3 ) 8
Quotient Rule for Exponents 9
4.1.2: Simplify Expressions with Positive Integer Exponents Examples: Simplify each expression. 1. 2. 3. 4. 5. x x 4 10 a a 7 8 7w 63w 5 8 b 8a b 32a 2 5 4 10 10 6 16 10
Product-Power Rule for Exponents (xy) 3 = (xy)(xy)(xy) = (x . x . x) . (y . y .y) = x 3 y 3 Examples: Simplify each expression. 1. (2x) 3 2. ( 4x) 4 11
Power Rule for Exponents (3 2 ) 3 = (3 2 )(3 2 )(3 2 ) = (3)(3)(3)(3)(3)(3) = 3 6 Examples: Simplify each expression.

#### You've reached the end of your free preview.

Want to read all 51 pages?

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern