Chapter 5: Exponents and Polynomials


 Mabel Lee
 4 years ago
 Views:
Transcription
1 Chapter 5: Exponents and Polynomials 5.1 Multiplication with Exponents and Scientific Notation 5.2 Division with Exponents 5.3 Operations with Monomials 5.4 Addition and Subtraction of Polynomials 5.5 Multiplication with Polynomials 5.6 Binomial Squares and other Special Products 5.7 Division with Polynomials 1
2 5.1 What is an Exponent? Consider Exercise: Write each expression as a single number. 2
3 Multiplication with Exponents Consider Method 1: (Order of Operations) Method 2: (Using Exponents) The Product Rule 3
4 Ex: Simplify 1) 4) 7) (w 3 z 4 )(w 3 z 7 ) 2) 5) 3) 6) (x + y) 6 (x + y) 9 4
5 Consider Method 1: (Order of Operations) Method 2: (Using Exponents) The Power Rule 5
6 Ex: Simplify 1) 3) 2) 4) [(x+y) 3 ] 27 6
7 Consider Method 1: (Order of Operations) Method 2: (Using Exponents) Raising a product to a power 7
8 Ex: Simplify 1) 3) 2) 8
9 Scientific Notation Definition: A number is in scientific notation when it is written as the product of a number between 1 and 10 and an integer power of 10. A number written in scientific notation takes the form: where and r is an integer. Examples Which are in scientific notation and which are not? 9
10 Scientific Notation Definition: A number is in scientific notation when it is written as the product of a number between 1 and 10 and an integer power of 10. A number written in scientific notation takes the form: where and r is an integer. Examples Write the following in scientific notation. 10
11 5.2 Division with Exponents Consider: Negative Exponents What is, for example? Using our product rule, we know that so, let's solve for in 11
12 Negative Exponent Rule and Examples Write each expression with a positive exponent. 12
13 Division with Exponents Consider Method 1: (Order of Operations) Method 2: (Using Exponents) The Quotient Rule 13
14 Ex: Simplify 1) 3) 5) (x+y) 9 (x+y) 2 2) 4) 14
15 Consider Raising a quotient to a power 15
16 Ex: Simplify 1) 3) 2) 16
17 Consider What should equal? By quotient rule, The Exponent Zero 17
18 Ex: Simplify 1) 3) 2) 4) 18
19 Application Suppose you have two squares, one of which is larger than the other. If the length of a side of the larger square is 3 times as long as the length of a side of the smaller square, how many of the smaller squares will it take to cover up the larger square? 19
20 Application Suppose you have two boxes, each of which is a cube. If the length of a side of the larger box is 3 times as long as the length of a side of the smaller box, how many of the smaller boxes will fit inside the larger box? 20
21 Scientific Notation with negative exponents Definition: A number in scientific notation with a negative exponent indicates a very small number. A number in scientific notation with a large positive integer indicates a large number. where and r is a negative integer. Examples Convert from scientific notation to decimal form. 21
22 Scientific Notation with negative exponents Definition: A number in scientific notation with a negative exponent indicates a very small number. A number in scientific notation with a large positive integer indicates a large number. where and r is a negative integer. Examples Write in scientific notation. 22
23 Definitions & Property of Exponents Overview 23
24 5.3 Operations with Monomials Definition: A monomial is a oneterm expression that is either a constant (number) or the product of a constant and one or more variables raised to whole number exponents. Examples 24
25 5.3 Operations with Monomials Definition: the degree of a monomial in onevariable is the exponent on the variable. If a monomial has multiple variables, the degree is the sum of all the exponents. Examples 25
26 5.3 Operations with Monomials Multiplying Monomials. (Which rule of exponents are you using?) Examples 26
27 5.3 Operations with Monomials Dividing Monomials. (Which rule of exponents are you using?) Examples Example Divide by 27
28 5.3 Operations with Monomials Examples Simplify 28
29 Multiplication and Division of Numbers written in Scientific Notation Examples Multiply Examples Divide Examples Simplify 29
30 Addition and Subtraction of Monomials Definition Two terms (monomials) with the same variable part (same variables raised to the same powers) are called similar or like terms. Examples Combine the like terms 30
31 Addition and Subtraction of Monomials Examples Simplify 31
32 Addition and Subtraction of Monomials Application A rectangular solid is twice as long as it is wide and onehalf as high as it is wide. Write an expression for the volume. 32
33 5.4 Addition and Subtraction of Polynomials Definition A polynomial is a finite sum of monomials (terms). Definition The degree of a polynomial is the degree of the leading term once the polynomial is written in standard form. (highest to lowest power) 33
34 5.4 Addition and Subtraction of Polynomials Examples: 1. Write the polynomial in standard form: 2. Find the value of when 3. Add: 4. Add and 34
35 5.4 Addition and Subtraction of Polynomials Examples: 5. Find the opposite polynomial to 6. Subtract: 7. Subtract from 35
36 Rule: Case 1: Product of Monomials 1) (5x)(3x) 36
37 Rule: 2) x(x  5) 37
38 Rule: 2) x(x  5) 3) 4x(x  5) 4) 4x(x  5) 38
39 Note the differences between addition/subtraction vs. multiplication 39
40 Consider (x + 3)(x + 2). Use the box method: Use the distributive property: 40
41 Consider (x + 3)(x + 2). 41
42 1) (x  3)(x + 2) 2) (x  5)(x  7) 3) (3x  4)(2x + 5) 4) (4x  1) (6x + 1) 42
43 Quick Check! (x  5) + (x + 2) (x  5)(x + 2) 43
44 44
45 45
46 Find the area & perimeter of the rectangle. 46
47 A. The Square of a Binomial. When both binomials are the same. Ex: Multiply and explore these products: Do you see a pattern? 47
48 Perfect Square Trinomials The Box Area Method The FOIL Method 48
49 Perfect Square Trinomials Ex: Identify A and B for each of the following: 49
50 Perfect Square Trinomials Ex: Use the formula to JUMP and write the result, 50
51 Mixed Exercises Ex: Simplify: 51
52 B. The Product of a Sum and a Difference when you have the SAME Two Numbers. Ex: Multiply and explore the products: Do you see a pattern? 52
53 Difference of two squares pattern (A + B)(A B) = A 2 B 2 The Box Area Method The FOIL Method 53
54 Difference of two squares pattern (A + B)(A B) = A 2 B 2 Ex: Identify the 'A' and 'B' in the following products. 54
55 Difference of two squares pattern (A + B)(A B) = A 2 B 2 Ex: Use the formula to JUMP and write the result,. 55
56 56
MathB65 Ch 4 IV, V, VI.notebook. October 31, 2017
Part 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest
More informationUnit 13: Polynomials and Exponents
Section 13.1: Polynomials Section 13.2: Operations on Polynomials Section 13.3: Properties of Exponents Section 13.4: Multiplication of Polynomials Section 13.5: Applications from Geometry Section 13.6:
More information5.3. Polynomials and Polynomial Functions
5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a
More informationName: Chapter 7: Exponents and Polynomials
Name: Chapter 7: Exponents and Polynomials 71: Integer Exponents Objectives: Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. You
More informationAlg 1B Chapter 7 Final Exam Review
Name: Class: Date: ID: A Alg B Chapter 7 Final Exam Review Please answer all questions and show your work. Simplify ( 2) 4. 2. Simplify ( 4) 4. 3. Simplify 5 2. 4. Simplify 9x0 y 3 z 8. 5. Simplify 7w0
More informationAlgebra I Unit Report Summary
Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit  ( Ascend Default unit) 1. A01_01_01 HAB.1 Word Phrases As Algebraic Expressions 2. A01_01_02
More informationReady To Go On? Skills Intervention 71 Integer Exponents
7A Evaluating Expressions with Zero and Negative Exponents Zero Exponent: Any nonzero number raised to the zero power is. 4 0 Ready To Go On? Skills Intervention 71 Integer Exponents Negative Exponent:
More informationSECTION 1.4 PolyNomiAls feet. Figure 1. A = s 2 = (2x) 2 = 4x 2 A = 2 (2x) 3 _ 2 = 1 _ = 3 _. A = lw = x 1. = x
SECTION 1.4 PolyNomiAls 4 1 learning ObjeCTIveS In this section, you will: Identify the degree and leading coefficient of polynomials. Add and subtract polynomials. Multiply polynomials. Use FOIL to multiply
More informationCHAPTER 1 POLYNOMIALS
1 CHAPTER 1 POLYNOMIALS 1.1 Removing Nested Symbols of Grouping Simplify. 1. 4x + 3( x ) + 4( x + 1). ( ) 3x + 4 5 x 3 + x 3. 3 5( y 4) + 6 y ( y + 3) 4. 3 n ( n + 5) 4 ( n + 8) 5. ( x + 5) x + 3( x 6)
More informationMath 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2
Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 April 11, 2016 Chapter 10 Section 1: Addition and Subtraction of Polynomials A monomial is
More informationMATH98 Intermediate Algebra Practice Test Form A
MATH98 Intermediate Algebra Practice Test Form A MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y  4)  (y + ) = 3y 1) A)
More informationBeginning Algebra MAT0024C. Professor Sikora. Professor M. J. Sikora ~ Valencia Community College
Beginning Algebra Professor Sikora MAT002C POLYNOMIALS 6.1 Positive Integer Exponents x n = x x x x x [n of these x factors] base exponent Numerical: Ex:  = where as Ex: () = Ex:  = and Ex: () = Rule:
More informationLesson 3 Algebraic expression:  the result obtained by applying operations (+, ,, ) to a collection of numbers and/or variables o
Lesson 3 Algebraic expression:  the result obtained by applying operations (+, ,, ) to a collection of numbers and/or variables o o ( 1)(9) 3 ( 1) 3 9 1 Evaluate the second expression at the left, if
More informationReview for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition.
LESSON 6 Review for Mastery Integer Exponents Remember that means 8. The base is, the exponent is positive. Exponents can also be 0 or negative. Zero Exponents Negative Exponents Negative Exponents in
More informationA2. Polynomials and Factoring. Section A2 1
A Polynomials and Factoring Section A 1 What you ll learn about Adding, Subtracting, and Multiplying Polynomials Special Products Factoring Polynomials Using Special Products Factoring Trinomials Factoring
More informationWe say that a polynomial is in the standard form if it is written in the order of decreasing exponents of x. Operations on polynomials:
R.4 Polynomials in one variable A monomial: an algebraic expression of the form ax n, where a is a real number, x is a variable and n is a nonnegative integer. : x,, 7 A binomial is the sum (or difference)
More informationMultiplication of Polynomials
Summary 391 Chapter 5 SUMMARY Section 5.1 A polynomial in x is defined by a finite sum of terms of the form ax n, where a is a real number and n is a whole number. a is the coefficient of the term. n is
More informationChapter Six. Polynomials. Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring
Chapter Six Polynomials Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring Properties of Exponents The properties below form the basis
More information5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014. c = Properites of Exponents. *Simplify each of the following:
48 5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014 Properites of Exponents 1. x a x b = x a+b *Simplify each of the following: a. x 4 x 8 = b. x 5 x 7 x = 2. xa xb = xa b c. 5 6 5 11 = d. x14
More informationUnit 2: Polynomials Guided Notes
Unit 2: Polynomials Guided Notes Name Period **If found, please return to Mrs. Brandley s room, M 8.** Self Assessment The following are the concepts you should know by the end of Unit 1. Periodically
More informationMATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline
MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline 1. Real Numbers (33 topics) 1.3 Fractions (pg. 27: 175 odd) A. Simplify fractions. B. Change mixed numbers
More informationAlgebra II Chapter 5: Polynomials and Polynomial Functions Part 1
Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Chapter 5 Lesson 1 Use Properties of Exponents Vocabulary Learn these! Love these! Know these! 1 Example 1: Evaluate Numerical Expressions
More informationSections 7.2, 7.3, 4.1
Sections 7., 7.3, 4.1 Section 7. Multiplying, Dividing and Simplifying Radicals This section will discuss the rules for multiplying, dividing and simplifying radicals. Product Rule for multiplying radicals
More informationWhen you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut.
Squaring a Binomial When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut. Solve. (x 3) 2 Step 1 Square the first term. Rules
More informationBeginning Algebra. 1. Review of PreAlgebra 1.1 Review of Integers 1.2 Review of Fractions
1. Review of PreAlgebra 1.1 Review of Integers 1.2 Review of Fractions Beginning Algebra 1.3 Review of Decimal Numbers and Square Roots 1.4 Review of Percents 1.5 Real Number System 1.6 Translations:
More informationPolynomials Practice Test
Name: Class: Date: Polynomials Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. From the list, which terms are like 7x? 7x 2, 6x, 5, 8x, 7x,
More informationSection 6.5 A General Factoring Strategy
Difference of Two Squares: a 2 b 2 = (a + b)(a b) NOTE: Sum of Two Squares, a 2 b 2, is not factorable Sum and Differences of Two Cubes: a 3 + b 3 = (a + b)(a 2 ab + b 2 ) a 3 b 3 = (a b)(a 2 + ab + b
More informationPOLYNOMIAL EXPRESSIONS PART 1
POLYNOMIAL EXPRESSIONS PART 1 A polynomial is an expression that is a sum of one or more terms. Each term consists of one or more variables multiplied by a coefficient. Coefficients can be negative, so
More informationHow to write polynomials in standard form How to add, subtract, and multiply polynomials How to use special products to multiply polynomials
PRC Ch P_3.notebook How to write polynomials in standard form How to add, subtract, and multiply polynomials How to use special products to multiply polynomials How to remove common factors from polynomials
More information27 Wyner Math 2 Spring 2019
27 Wyner Math 2 Spring 2019 CHAPTER SIX: POLYNOMIALS Review January 25 Test February 8 Thorough understanding and fluency of the concepts and methods in this chapter is a cornerstone to success in the
More informationNAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4
Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as
More information6.1 Using Properties of Exponents 1. Use properties of exponents to evaluate and simplify expressions involving powers. Product of Powers Property
6.1 Using Properties of Exponents Objectives 1. Use properties of exponents to evaluate and simplify expressions involving powers. 2. Use exponents and scientific notation to solve real life problems.
More informationUnit 2: Polynomials Guided Notes
Unit 2: Polynomials Guided Notes Name Period **If found, please return to Mrs. Brandley s room, M 8.** Self Assessment The following are the concepts you should know by the end of Unit 1. Periodically
More informationDay 131 Practice. What Can You Do With Polynomials?
Polynomials Monomial  a Number, a Variable or a PRODUCT of a number and a variable. Monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree
More informationFind two positive factors of 24 whose sum is 10. Make an organized list.
9.5 Study Guide For use with pages 582 589 GOAL Factor trinomials of the form x 2 1 bx 1 c. EXAMPLE 1 Factor when b and c are positive Factor x 2 1 10x 1 24. Find two positive factors of 24 whose sum is
More informationMATHEMATICS 9 CHAPTER 7 MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT NAME: DATE: BLOCK: TEACHER: Miller High School Mathematics Page 1
MATHEMATICS 9 CHAPTER 7 NAME: DATE: BLOCK: TEACHER: MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT Miller High School Mathematics Page 1 Day 1: Creating expressions with algebra tiles 1. Determine the multiplication
More informationChapter 6. Polynomials
Chapter 6 Polynomials How to Play the Stock Market 6.1 Monomials: Multiplication and Division 6.2 Polynomials 6.3 Addition and Subtraction of Polynomials 6.4 Multiplication of Polynomials Chapter Review
More informationAdding & Subtracting Polynomial Expressions
Adding & Subtracting Polynomial Expressions A polynomial is a single term or the sum of two or more terms containing variables with exponents that are positive integers. Polynomials are ADDED or SUBTRACTED
More informationMath 10C Polynomials Concept Sheets
Math 10C Polynomials Concept Sheets Concept 1: Polynomial Intro & Review A polynomial is a mathematical expression with one or more terms in which the exponents are whole numbers and the coefficients
More informationProperties of Real Numbers
PreAlgebra Properties of Real Numbers Identity Properties Addition: Multiplication: Commutative Properties Addition: Multiplication: Associative Properties Inverse Properties Distributive Properties Properties
More informationreview To find the coefficient of all the terms in 15ab + 60bc 17ca: Coefficient of ab = 15 Coefficient of bc = 60 Coefficient of ca = 17
1. Revision Recall basic terms of algebraic expressions like Variable, Constant, Term, Coefficient, Polynomial etc. The coefficients of the terms in 4x 2 5xy + 6y 2 are Coefficient of 4x 2 is 4 Coefficient
More informationTopic 7: Polynomials. Introduction to Polynomials. Table of Contents. Vocab. Degree of a Polynomial. Vocab. A. 11x 7 + 3x 3
Topic 7: Polynomials Table of Contents 1. Introduction to Polynomials. Adding & Subtracting Polynomials 3. Multiplying Polynomials 4. Special Products of Binomials 5. Factoring Polynomials 6. Factoring
More informationUNIT 2 FACTORING. M2 Ch 11 all
UNIT 2 FACTORING M2 Ch 11 all 2.1 Polynomials Objective I will be able to put polynomials in standard form and identify their degree and type. I will be able to add and subtract polynomials. Vocabulary
More information77 Multiplying Polynomials
Example 1: Multiplying Monomials A. (6y 3 )(3y 5 ) (6y 3 )(3y 5 ) (6 3)(y 3 y 5 ) 18y 8 Group factors with like bases together. B. (3mn 2 ) (9m 2 n) Example 1C: Multiplying Monomials Group factors with
More informationNever leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!!
1 ICM Unit 0 Algebra Rules Lesson 1 Rules of Exponents RULE EXAMPLE EXPLANANTION a m a n = a m+n A) x x 6 = B) x 4 y 8 x 3 yz = When multiplying with like bases, keep the base and add the exponents. a
More information1.3 Algebraic Expressions. Copyright Cengage Learning. All rights reserved.
1.3 Algebraic Expressions Copyright Cengage Learning. All rights reserved. Objectives Adding and Subtracting Polynomials Multiplying Algebraic Expressions Special Product Formulas Factoring Common Factors
More informationLESSON 9.1 ROOTS AND RADICALS
LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical
More informationSections 7.1, 7.2: Sums, differences, products of polynomials CHAPTER 7: POLYNOMIALS
Sections 7.1, 7.2: Sums, differences, products of polynomials CHAPTER 7: POLYNOMIALS Quiz results Average 73%: high h score 100% Problems: Keeping track of negative signs x = + = + Function notation f(x)
More informationMATH98 Intermediate Algebra Practice Test Form B
MATH98 Intermediate Algebra Practice Test Form B MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y  4)  (y + 9) = y 1) 
More informationMATH Spring 2010 Topics per Section
MATH 101  Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line
More informationRising 8th Grade Math. Algebra 1 Summer Review Packet
Rising 8th Grade Math Algebra 1 Summer Review Packet 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving MultiStep Equations 3. Add/subtract
More informationUnit 3 Factors & Products
1 Unit 3 Factors & Products General Outcome: Develop algebraic reasoning and number sense. Specific Outcomes: 3.1 Demonstrate an understanding of factors of whole number by determining the: o prime factors
More informationMath 0320 Final Exam Review
Math 0320 Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Factor out the GCF using the Distributive Property. 1) 6x 3 + 9x 1) Objective:
More informationSomething that can have different values at different times. A variable is usually represented by a letter in algebraic expressions.
Lesson Objectives: Students will be able to define, recognize and use the following terms in the context of polynomials: o Constant o Variable o Monomial o Binomial o Trinomial o Polynomial o Numerical
More informationUnit 1 Vocabulary. A function that contains 1 or more or terms. The variables may be to any nonnegative power.
MODULE 1 1 Polynomial A function that contains 1 or more or terms. The variables may be to any nonnegative power. 1 Modeling Mathematical modeling is the process of using, and to represent real world
More informationPrerequisites. Introduction CHAPTER OUTLINE
Prerequisites 1 Figure 1 Credit: Andreas Kambanls CHAPTER OUTLINE 1.1 Real Numbers: Algebra Essentials 1.2 Exponents and Scientific Notation 1.3 Radicals and Rational Expressions 1.4 Polynomials 1.5 Factoring
More information{ independent variable some property or restriction about independent variable } where the vertical line is read such that.
Page 1 of 5 Introduction to Review Materials One key to Algebra success is identifying the type of work necessary to answer a specific question. First you need to identify whether you are dealing with
More informationChapter 8 Polynomials and Factoring
Chapter 8 Polynomials and Factoring 8.1 Add and Subtract Polynomials Monomial A. EX: Degree of a monomial the of all of the of the EX: 4x 2 y Polynomial A or EX: Degree of a polynomial the of its terms
More informationSolving MultiStep Equations
1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving MultiStep Equations 3. Add/subtract terms to both sides of the equation to get the
More informationAlgebra 1: Hutschenreuter Chapter 10 Notes Adding and Subtracting Polynomials
Algebra 1: Hutschenreuter Chapter 10 Notes Name 10.1 Adding and Subtracting Polynomials Polynomial an expression where terms are being either added and/or subtracted together Ex: 6x 4 + 3x 3 + 5x 2 +
More informationUnit 7: Factoring Quadratic Polynomials
Unit 7: Factoring Quadratic Polynomials A polynomial is represented by: where the coefficients are real numbers and the exponents are nonnegative integers. Side Note: Examples of real numbers: Examples
More informationReal Numbers. Real numbers are divided into two types, rational numbers and irrational numbers
Real Numbers Real numbers are divided into two types, rational numbers and irrational numbers I. Rational Numbers: Any number that can be expressed as the quotient of two integers. (fraction). Any number
More information5.2. Adding and Subtracting Polynomials. Objectives. Know the basic definitions for polynomials. Add and subtract polynomials.
Chapter 5 Section 2 5.2 Adding and Subtracting Polynomials Objectives 1 2 Know the basic definitions for polynomials. Add and subtract polynomials. Objective 1 Know the basic definitions for polynomials.
More informationUnit 1 Foundations of Algebra
1 Unit 1 Foundations of Algebra Real Number System 2 A. Real Number System 1. Counting Numbers (Natural Numbers) {1,2,3,4, } 2. Whole Numbers { 0,1,2,3,4, } 3. Integers  Negative and Positive Whole Numbers
More informationPolynomial comes from poly (meaning "many") and nomial (in this case meaning "term")... so it says "many terms
Polynomials Polynomial comes from poly (meaning "many") and nomial (in this case meaning "term")... so it says "many terms Polynomials A polynomial looks like this: Term A number, a variable, or the
More informationMath 0312 EXAM 2 Review Questions
Name Decide whether the ordered pair is a solution of the given system. 1. 4x + y = 2 2x + 4y = 20 ; (2, 6) Solve the system by graphing. 2. x  y = 6 x + y = 16 Solve the system by substitution. If
More informationAlgebra 1 Unit 6B Factoring
Algebra 1 Unit 6B Factoring Monday Tuesday Wednesday Thursday Friday 9 A Day 10 B Day 11 A Day 12 B Day 13 A Day Test Exponents and Polynomials Factor GCF and Trinomials box method Factoring Trinomials
More informationMAFS Algebra 1. Polynomials. Day 15  Student Packet
MAFS Algebra 1 Polynomials Day 15  Student Packet Day 15: Polynomials MAFS.91.ASSE.1., MAFS.91.ASSE..3a,b, MAFS.91.AAPR..3, MAFS.91.FIF.3.7c I CAN rewrite algebraic expressions in different equivalent
More informationChapter 3: Section 3.1: Factors & Multiples of Whole Numbers
Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Prime Factor: a prime number that is a factor of a number. The first 15 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
More informationAlgebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals
Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive
More informationUnderstand the vocabulary used to describe polynomials Add polynomials Subtract polynomials Graph equations defined by polynomials of degree 2
Section 5.1: ADDING AND SUBTRACTING POLYNOMIALS When you are done with your homework you should be able to Understand the vocabulary used to describe polynomials Add polynomials Subtract polynomials Graph
More informationA monomial is measured by its degree To find its degree, we add up the exponents of all the variables of the monomial.
UNIT 6 POLYNOMIALS Polynomial (Definition) A monomial or a sum of monomials. A monomial is measured by its degree To find its degree, we add up the exponents of all the variables of the monomial. Ex. 2
More informationLesson 3: Polynomials and Exponents, Part 1
Lesson 2: Introduction to Variables Assessment Lesson 3: Polynomials and Exponents, Part 1 When working with algebraic expressions, variables raised to a power play a major role. In this lesson, we look
More informationMathwithsheppard.weebly.com
Unit #: Powers and Polynomials Unit Outline: Date Lesson Title Assignment Completed.1 Introduction to Algebra. Discovering the Exponent Laws Part 1. Discovering the Exponent Laws Part. Multiplying and
More informationAlgebra 1B Final Review
Name: Class: Date: ID: A Algebra 1B Final Review Short Answer 1. Originally a rectangle was twice as long as it was wide. When 5 m was subtracted from its length and 3 m subtracted from its width, the
More informationTABLE OF CONTENTS. Introduction to Finish Line Indiana Math 10. UNIT 1: Number Sense, Expressions, and Computation. Real Numbers
TABLE OF CONTENTS Introduction to Finish Line Indiana Math 10 UNIT 1: Number Sense, Expressions, and Computation LESSON 1 8.NS.1, 8.NS.2, A1.RNE.1, A1.RNE.2 LESSON 2 8.NS.3, 8.NS.4 LESSON 3 A1.RNE.3 LESSON
More informationLinear Equations & Inequalities Definitions
Linear Equations & Inequalities Definitions Constants  a term that is only a number Example: 3; 6; 10.5 Coefficients  the number in front of a term Example: 3x 2, 3 is the coefficient Variable 
More information1 of 32 4/24/2018, 11:38 AM
1 of 3 4/4/018, 11:38 AM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework149aleks 1 Insert < or > between the pair of integers to make the statement
More informationMathB65 Ch 4 VII, VIII, IX.notebook. November 06, 2017
Chapter 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest
More informationDay 7: Polynomials MAFS.912.ASSE.1.2, MAFS.912.ASSE.2.3a,b, MAFS.912.AAPR.2.3, MAFS.912.FIF.3.7c
Day 7: Polynomials MAFS.91.ASSE.1., MAFS.91.ASSE..3a,b, MAFS.91.AAPR..3, MAFS.91.FIF.3.7c I CAN rewrite algebraic expressions in different equivalent forms using factoring techniques use equivalent
More informationPOLYNOMIAL: A polynomial is a or the
MONOMIALS: CC Math I Standards: Unit 6 POLYNOMIALS: INTRODUCTION EXAMPLES: A number 4 y a 1 x y A variable NONEXAMPLES: Variable as an exponent A sum x x 3 The product of variables 5a The product of numbers
More informationCollecting Like Terms
MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARMUP Example 1: Simplify each expression using exponent laws.
More informationAlgebra. Practice Pack
Algebra Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Algebra Basics Practice 1 What Are Negative and Positive Numbers?... 1 Practice 2 Larger and Smaller Numbers................ 2 Practice
More informationPolynomials: Add and Subtract
GSE Advanced Algebra Operations with Polynomials Polynomials: Add and Subtract Let's do a quick review on what polynomials are and the types of polynomials. A monomial is an algebraic expression that is
More informationNote: A file Algebra Unit 09 Practice X Patterns can be useful to prepare students to quickly find sum and product.
Note: This unit can be used as needed (review or introductory) to practice operations on polynomials. Math Background Previously, you Identified monomials and their characteristics Applied the laws of
More informationAccuplacer Review Workshop. Elementary Algebra Part II. Week Three. Includes internet links to instructional videos for additional resources:
Accuplacer Review Workshop Elementary Algebra Part II Week Three Includes internet links to instructional videos for additional resources: http://www.mathispower4u.com (Arithmetic Video Library) http://www.purplemath.com
More informationFastTrack  MA109. Exponents and Review of Polynomials
FastTrack  MA109 Exponents and Review of Polynomials Katherine Paullin, Ph.D. Lecturer, Department of Mathematics University of Kentucky katherine.paullin@uky.edu Monday, August 15, 2016 1 / 25 REEF Question
More informationI CAN classify polynomials by degree and by the number of terms.
131 Polynomials I CAN classify polynomials by degree and by the number of terms. 131 Polynomials Insert Lesson Title Here Vocabulary monomial polynomial binomial trinomial degree of a polynomial 131
More informationLesson 6. Diana Pell. Monday, March 17. Section 4.1: Solve Linear Inequalities Using Properties of Inequality
Lesson 6 Diana Pell Monday, March 17 Section 4.1: Solve Linear Inequalities Using Properties of Inequality Example 1. Solve each inequality. Graph the solution set and write it using interval notation.
More informationSection 5.1 Polynomial Functions and Models
Term: A term is an expression that involves only multiplication and/or division with constants and/or variables. A term is separated by + or Polynomial: A polynomial is a single term or the sum of two
More informationTopics Covered in Math 115
Topics Covered in Math 115 Basic Concepts Integer Exponents Use bases and exponents. Evaluate exponential expressions. Apply the product, quotient, and power rules. Polynomial Expressions Perform addition
More informationMath 1 Variable Manipulation Part 6 Polynomials
Name: Math 1 Variable Manipulation Part 6 Polynomials Date: 1 VOCABULARY Constant: A term that does not have a variable is called a constant. Example: the number 5 is a constant because it does not have
More informationUnit 2: Polynomials Guided Notes
Unit 2: Polynomials Guided Notes Name Period **If found, please return to Mrs. Brandley s room, M8.** 1 SelfAssessment The following are the concepts you should know by the end of Unit 1. Periodically
More informationUnit 1 Notes. Polynomials
Unit 1 Notes 1 Day Number Date Topic Problem Set 1 Wed. Sept. Operations with Signed Numbers and Order of Operations PreUnit Review PS (1 ) Thurs. Sept. Working with Exponents Start Exponent Laws P.S.
More informationJohn L. Lehet
New! Android App! SAT Mathematics Review Algebra John L. Lehet jlehet@mathmaverick.com www.mathmaverick.com SAT Math Daily Question Android App  new question each day  archive of over 200 questions 
More informationP.1: Algebraic Expressions, Mathematical Models, and Real Numbers
Chapter P Prerequisites: Fundamental Concepts of Algebra Precalculus notes Date: P.1: Algebraic Expressions, Mathematical Models, and Real Numbers Algebraic expression: a combination of variables and
More informationAlgebra I. Exponents and Polynomials. Name
Algebra I Exponents and Polynomials Name 1 2 UNIT SELFTEST QUESTIONS The Unit Organizer #6 2 LAST UNIT /Experience NAME 4 BIGGER PICTURE DATE Operations with Numbers and Variables 1 CURRENT CURRENT UNIT
More informationThe number part of a term with a variable part. Terms that have the same variable parts. Constant terms are also like terms.
Algebra Notes Section 9.1: Add and Subtract Polynomials Objective(s): To be able to add and subtract polynomials. Recall: Coefficient (p. 97): Term of a polynomial (p. 97): Like Terms (p. 97): The number
More informationDue for this week. Slide 2. Copyright 2009 Pearson Education, Inc. Publishing as Pearson AddisonWesley
MTH 09 Week 1 Due for this week Homework 1 (on MyMathLab via the Materials Link) The fifth night after class at 11:59pm. Read Chapter 6.16.4, Do the MyMathLab SelfCheck for week 1. Learning team coordination/connections.
More information51 Study Guide and Intervention
51 Study Guide and Intervention Multiply and Divide Monomials Negative exponents are a way of expressing the multiplicative inverse of a number. Negative Exponents a n = 1 a n and 1 a n = a n for any
More information