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Contents Lesson 5-1Monomials Lesson 5-2Polynomials Lesson 5-3Dividing Polynomials Lesson 5-4Factoring Polynomials Lesson 5-5Roots of Real Numbers Lesson 5-6Radical Expressions Lesson 5-7Rational Exponents Lesson 5-8Radical Equations and Inequalities Lesson 5-9Complex Numbers

Lesson 1 Contents Example 1Simplify Expressions with Multiplication Example 2Simplify Expressions with Division Example 3Simplify Expressions with Powers Example 4Simplify Expressions Using Several Properties Example 5Express Numbers in Scientific Notation Example 6Multiply Numbers in Scientific Notation Example 7Divide Numbers in Scientific Notation

Example 1-1a Commutative Property Answer:Definition of exponents

Example 1-1b Answer:

Example 1-2a Subtract exponents. Remember that a simplified expression cannot contain negative exponents. Answer:Simplify

Example 1-2b Answer:

Example 1-3a Power of a power Answer:

Example 1-3b Power of a power Answer:

Example 1-3c Power of a product Power of a quotient Answer:

Example 1-3d Negative exponent Power of a quotient Answer:

Simplify each expression. a. b. c. d. Example 1-3e Answer:

Example 1-4a Method 1 Raise the numerator and the denominator to the fifth power before simplifying.

Example 1-4a Answer:

Example 1-4b Method 2 Simplify the fraction before raising to the fifth power. Answer:

Example 1-4c Answer:

Example 1-5a Express 4, 560, 000 in scientific notation. 4,560,000 Answer: Write 1, 000, 000 as a power of 10.

Example 1-5b Express in scientific notation. Use a negative exponent. Answer:

Express each number in scientific notation. a. 52, 000 b Example 1-5c Answer:

Express the result in scientific notation. Example 1-6a Associative and Commutative Properties Answer:

Associative and Commutative Properties Example 1-6b Express the result in scientific notation. Answer:

Evaluate. Express the result in scientific notation. a. b. Example 1-6c Answer:

Example 1-7a Divide the number of red blood cells in the sample by the number of red blood cells in 1 milliliter of blood. Answer: There are about 1.66 milliliters of blood in the sample. Biology There are about red blood cells in one milliliter of blood. A certain blood sample contains red blood cells. About how many milliliters of blood are in the sample?  number of red blood cells in sample  number of red blood cells in 1 milliliter

Example 1-7b Answer: Biology A petri dish started withgerms in it. A half hour later, there are How many times as great is the amount a half hour later?

End of Lesson 1

Lesson 2 Contents Example 1Degree of a Polynomial Example 2Subtract and Simplify Example 3Multiply and Simplify Example 4Multiply Two Binomials Example 5Multiply Polynomials

Example 2-1a Determine whether is a polynomial. If it is a polynomial, state the degree of the polynomial. Answer: This expression is not a polynomial because is not a monomial.

Example 2-1b Answer: This expression is a polynomial because each term is a monomial. The degree of the first term is 5 and the degree of the second term is or 9. The degree of the polynomial is 9. Determine whether is a polynomial. If it is a polynomial, state the degree of the polynomial.

Determine whether each expression is a polynomial. If it is a polynomial, state the degree of the polynomial. a. b. Example 2-1c Answer: yes, 5 Answer: no

Example 2-2a Simplify Distribute the –1. Group like terms. Combine like terms.Answer:

Example 2-2b Simplify Answer:

Example 2-3a Distributive Property Answer: Multiply the monomials.

Example 2-3b Answer:

Example 2-4a Outer termsInner termsLast termsFirst terms Answer: Multiply monomials and add like terms. +++

Example 2-4b Answer:

Example 2-5a Distributive Property Multiply monomials. Answer: Combine like terms.

Example 2-5b Answer:

End of Lesson 2