Section 4 1 The Product Quotient and Power

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Section 4. 1 The Product, Quotient, and Power Rules for Exponents

Section 4. 1 The Product, Quotient, and Power Rules for Exponents

OBJECTIV ES A Multiply expressions using the product rule for exponents.

OBJECTIV ES A Multiply expressions using the product rule for exponents.

OBJECTIV ES B Divide expressions using the quotient rule for exponents.

OBJECTIV ES B Divide expressions using the quotient rule for exponents.

OBJECTIV ES C Use the power rules to simplify expressions.

OBJECTIV ES C Use the power rules to simplify expressions.

RULES Signs for Multiplication 1. When multiplying two numbers with the same sign, product

RULES Signs for Multiplication 1. When multiplying two numbers with the same sign, product is positive (+).

RULES Signs for Multiplication 2. When multiplying two numbers with different signs, product is

RULES Signs for Multiplication 2. When multiplying two numbers with different signs, product is negative (-).

RULES Signs for Division 1. When dividing two numbers with the same sign, product

RULES Signs for Division 1. When dividing two numbers with the same sign, product is positive (+).

RULES Signs for Division 2. When dividing two numbers with different signs, product is

RULES Signs for Division 2. When dividing two numbers with different signs, product is negative (-).

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 1. Product

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 1. Product rule for exponents Exampl e:

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 2. Quotient

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 2. Quotient rule for exponents

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 2. Quotient

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 2. Quotient rule for exponents Exampl e:

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 3. Power

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 3. Power rule for products

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 3. Power

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 3. Power rule for products Example:

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 4. Power

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 4. Power rule for quotients

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 4. Power

RULES FOR If m, n, EXPONENTS and k are positive integers, then: 4. Power rule for quotients Example:

Chapter 4 Exponents and Polynomials Section 4. 1 Exercise #1

Chapter 4 Exponents and Polynomials Section 4. 1 Exercise #1

Chapter 4 Exponents and Polynomials Section 4. 1 Exercise #2

Chapter 4 Exponents and Polynomials Section 4. 1 Exercise #2

Section 4. 2 Integer Exponents

Section 4. 2 Integer Exponents

OBJECTIV ES A Write an expression with negative exponents as an equivalent one with

OBJECTIV ES A Write an expression with negative exponents as an equivalent one with positive exponents.

OBJECTIV ES B Write a fraction involving exponents as a number with a negative

OBJECTIV ES B Write a fraction involving exponents as a number with a negative power.

OBJECTIV ES C Multiply and divide expressions involving negative exponents.

OBJECTIV ES C Multiply and divide expressions involving negative exponents.

RULES Zero Exponent Negative Exponent If n is a positive integer,

RULES Zero Exponent Negative Exponent If n is a positive integer,

RULES th n Power of a Quotient

RULES th n Power of a Quotient

RULES Simplifying Fractions with Negative Exponents For any nonzero numbers x and y and

RULES Simplifying Fractions with Negative Exponents For any nonzero numbers x and y and any positive integers m and n:

Chapter 4 Exponents and Polynomials Section 4. 2 Exercise #4

Chapter 4 Exponents and Polynomials Section 4. 2 Exercise #4

Simplify and write the answer without negative exponents.

Simplify and write the answer without negative exponents.

Simplify and write the answer without negative exponents.

Simplify and write the answer without negative exponents.

Chapter 4 Exponents and Polynomials Section 4. 2 Exercise #5

Chapter 4 Exponents and Polynomials Section 4. 2 Exercise #5

Section 4. 3 Application of Exponents: Scientific Notation

Section 4. 3 Application of Exponents: Scientific Notation

OBJECTIV ES A Write numbers in scientific notation.

OBJECTIV ES A Write numbers in scientific notation.

OBJECTIV ES B Multiply and divide numbers in scientific notation. C Solve applications.

OBJECTIV ES B Multiply and divide numbers in scientific notation. C Solve applications.

RULES A number in scientific notation is written as Where M is a number

RULES A number in scientific notation is written as Where M is a number between 1 and 10 and n is an integer.

PROCEDURE Writing a number in scientific notation 1. Move decimal point in number so

PROCEDURE Writing a number in scientific notation 1. Move decimal point in number so there is only one nonzero digit to its left. The resulting number is M

PROCEDURE Writing a number in scientific notation 2. If the decimal point is moved

PROCEDURE Writing a number in scientific notation 2. If the decimal point is moved to the left, n is positive; If the decimal point is moved to the right, n is negative.

PROCEDURE Writing a number in scientific notation

PROCEDURE Writing a number in scientific notation

PROCEDURE Multiplying using scientific notation 1. Multiply decimal parts first. Write result in scientific

PROCEDURE Multiplying using scientific notation 1. Multiply decimal parts first. Write result in scientific notation.

PROCEDURE Multiplying using scientific notation 2. Multiply powers of 10 using product rule.

PROCEDURE Multiplying using scientific notation 2. Multiply powers of 10 using product rule.

PROCEDURE Multiplying using scientific notation 3. Answer is product obtained in steps 1 and

PROCEDURE Multiplying using scientific notation 3. Answer is product obtained in steps 1 and 2 after simplification.

Chapter 4 Exponents and Polynomials Section 4. 3 Exercise #6

Chapter 4 Exponents and Polynomials Section 4. 3 Exercise #6

Write in scientific notation.

Write in scientific notation.

Chapter 4 Exponents and Polynomials Section 4. 3 Exercise #7

Chapter 4 Exponents and Polynomials Section 4. 3 Exercise #7

Perform the indicated operations.

Perform the indicated operations.

Section 4. 4 Polynomials: An Introduction

Section 4. 4 Polynomials: An Introduction

OBJECTIV ES A Classify B polynomials. Find the degree of a polynomial.

OBJECTIV ES A Classify B polynomials. Find the degree of a polynomial.

OBJECTIV ES C Write a polynomial in descending order. D Evaluate polynomials.

OBJECTIV ES C Write a polynomial in descending order. D Evaluate polynomials.

DEFINITION Polynomial An algebraic expression formed using addition and subtraction on products of numbers

DEFINITION Polynomial An algebraic expression formed using addition and subtraction on products of numbers and variables raised to whole number

Chapter 4 Exponents and Polynomials Section 4. 4 Exercise #8

Chapter 4 Exponents and Polynomials Section 4. 4 Exercise #8

Classify as a monomial (M), binomial (B), or trinomial (T). B, binomial M, monomial

Classify as a monomial (M), binomial (B), or trinomial (T). B, binomial M, monomial T, trinomial

Chapter 4 Exponents and Polynomials Section 4. 4 Exercise #10

Chapter 4 Exponents and Polynomials Section 4. 4 Exercise #10

Find the value.

Find the value.

Section 4. 5 Addition and Subtraction of Polynomials

Section 4. 5 Addition and Subtraction of Polynomials

OBJECTIV ES A Add polynomials. B Subtract polynomials.

OBJECTIV ES A Add polynomials. B Subtract polynomials.

OBJECTIV ES C Find areas by adding polynomials. D Solve applications.

OBJECTIV ES C Find areas by adding polynomials. D Solve applications.

Chapter 4 Exponents and Polynomials Section 4. 5 Exercise #11

Chapter 4 Exponents and Polynomials Section 4. 5 Exercise #11

Add.

Add.

Chapter 4 Exponents and Polynomials Section 4. 5 Exercise #12

Chapter 4 Exponents and Polynomials Section 4. 5 Exercise #12

Section 4. 6 Multiplication of Polynomials

Section 4. 6 Multiplication of Polynomials

OBJECTIV ES A B Multiply two monomials. Multiply a monomial and a binomial.

OBJECTIV ES A B Multiply two monomials. Multiply a monomial and a binomial.

OBJECTIV ES C Multiply two D binomials using FOIL method. Solve an application.

OBJECTIV ES C Multiply two D binomials using FOIL method. Solve an application.

PROCEDURE FOIL Method for Multiplying Binomials First terms multiplied first. Outer terms multiplied second.

PROCEDURE FOIL Method for Multiplying Binomials First terms multiplied first. Outer terms multiplied second. Inner terms multiplied third. Last terms multiplied

Chapter 4 Exponents and Polynomials Section 4. 6 Exercise #16

Chapter 4 Exponents and Polynomials Section 4. 6 Exercise #16

F L O I

F L O I

Section 4. 7 Special Product of Polynomials

Section 4. 7 Special Product of Polynomials

OBJECTIV ES Expand binomials of the form A B C

OBJECTIV ES Expand binomials of the form A B C

OBJECTIV ES D Multiply a binomial by a trinomial. E Multiply any two polynomials.

OBJECTIV ES D Multiply a binomial by a trinomial. E Multiply any two polynomials.

SPECIAL PRODUCTS

SPECIAL PRODUCTS

SPECIAL PRODUCTS

SPECIAL PRODUCTS

SPECIAL PRODUCTS

SPECIAL PRODUCTS

SPECIAL PRODUCTS

SPECIAL PRODUCTS

PROCEDURE Multiplying Any Two Polynomials (Term-By-Term Multiplication) Multiply each term of one by every

PROCEDURE Multiplying Any Two Polynomials (Term-By-Term Multiplication) Multiply each term of one by every term of other and add results.

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 1. Is the product the square of

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 1. Is the product the square of a binomial? If so, use SP 2 or SP 3. Both answers have three

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 2. Are the two binomials in the

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 2. Are the two binomials in the product the sum and difference of the same two terms?

PROCEDURE Appropriate Method for Multiplying Two Polynomials: If so, use SP 4. Answer has

PROCEDURE Appropriate Method for Multiplying Two Polynomials: If so, use SP 4. Answer has two terms.

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 3. Is the binomial product different from

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 3. Is the binomial product different from previous two? If so, use FOIL. Answer has three or four

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 4. Is product still different? If so,

PROCEDURE Appropriate Method for Multiplying Two Polynomials: 4. Is product still different? If so, multiply every term of first polynomial by every term of second

Chapter 4 Exponents and Polynomials Section 4. 7 Exercise #18

Chapter 4 Exponents and Polynomials Section 4. 7 Exercise #18

Expand.

Expand.

Chapter 4 Exponents and Polynomials Section 4. 7 Exercise #19

Chapter 4 Exponents and Polynomials Section 4. 7 Exercise #19

Chapter 4 Exponents and Polynomials Section 4. 7 Exercise #20

Chapter 4 Exponents and Polynomials Section 4. 7 Exercise #20

Find

Find

Section 4. 8 Division of Polynomials

Section 4. 8 Division of Polynomials

OBJECTIV ES A Divide a polynomial by a monomial. B Divide one polynomial by

OBJECTIV ES A Divide a polynomial by a monomial. B Divide one polynomial by another polynomial.

RULE To Divide A Polynomial By A Monomial Divide each term in polynomial by

RULE To Divide A Polynomial By A Monomial Divide each term in polynomial by monomial.

Chapter 4 Exponents and Polynomials Section 4. 8 Exercise #25

Chapter 4 Exponents and Polynomials Section 4. 8 Exercise #25

Divide.

Divide.