Adding and Subtracting Polynomials
|
|
- Janel Hunt
- 6 years ago
- Views:
Transcription
1 Exploratory Exercise Kim was working on a problem in math when she ran across this problem. Distribute and simplify if possible. 2(3x + 5) Kim s dad said, I remember doing something like this in school. He then drew two arcs on her paper. Distribute and simplify if possible. 2(3x + 5) 1. Talk to your partner about what Kim s dad was trying to show. Then complete Kim s problem. In Lesson 7, you mainly used the commutative and associative properties, and only looked at examples of the distributive property. In this lesson we ll look closer at the distributive property and then in the next lesson you ll extend your knowledge about this important property. 2. What does the word distribute mean? Give two examples of the word in everyday use. 3. In math, distribute means to multiply out the parts of an expression. How does this definition relate to your definition from Exercise 2? S.67
2 4. In each example below, one or more mistakes were made when distributing. Circle the mistakes and then write the correct expression. A. 2(3x + 5) = 6x + 5 B. 2 x(2x 3) = x C. 3(3x + 4) = 9x + 4 D. 4(4x 5) = 16x 20 E. 2 2(4x + 6) = + 2 8x 12 F. 3 x(4x 5x+ 6) = x x x 5. What was the common mistake made in 4A, 4B and 4C? 6. What was the common mistake made in 4D, 4E and 4F? S.68
3 ADDING POLYNOMIALS 7. Add the following polynomials by combining like terms. Be careful you will have to distribute in a few of them. A. (3x+ 5) + (7x 3) B. 2 (2x 3) + (7x+ 2) C. (3x+ 4) + ( 4x 7) D. (4x 5) + 2(3x+ 1) E (4x + 6) + (7x 9x+ 3) F. 3 2 x(4x 5x+ 6) + (6x + 7x 3) SUBTRACTING POLYNOMIALS When subtracting polynomials, you will need to distribute the negative sign to all the terms in the parentheses. 8. Subtract these polynomials and then combine like terms. A. 2 2 (8x 9) (6x 2) B. (5x 2) (3x+ 9) C. 5( x+ 1) 6( x 1) D. 6x 5 (5x 6) E x 20 2(10x 5x+ 7) F x x(8x + 9x 4) S.69
4 9. Determine which word matches each definition. Word Bank Polynomial Monomial Binomial Trinomial Degree of a Term Degree of a Polynomial Standard Form of a Polynomial Definition Word A. The sum of the exponents of the variable symbols that appear in the monomial B. A polynomial with only two terms C. The sum (or difference) of monomials D. The degree of the monomial term with the highest degree E. The terms are rewritten so that the terms are in order from greatest degree to least degree F. An algebraic expression generated using only the multiplication operator ( ). Thus, it does not contain + or operators. G. A polynomial with only three terms 10. Go back to Exercises 7 and 8 and write each polynomial in standard form, if it isn t already in standard form, and then determine the degree of the resulting polynomial. 11. Janie writes a polynomial expression using only one variable, xx, with degree 3. Max writes a polynomial expression using only one variable, xx, with degree 7. A. What can you determine about the degree of the sum of Janie s and Max s polynomials? B. What can you determine about the degree of the difference of Janie s and Max s polynomials? S.70
5 Homework Problem Set 1. Find each sum or difference by combining the parts that are alike. A. (4xx 2 + xx + 7) + (2xx 2 + 3xx + 1) B. (3xx 3 xx 2 + 8) (xx 3 + 5xx 2 + 4xx 7) C. 3(xx 3 + 8xx) 2(xx ) D. (5 tt tt 2 ) + (9tt + tt 2 ) E. (3pp + 1) + 6(pp 8) (pp + 2) 2. Celina says that each of the following expressions is actually a binomial in disguise. For example, she sees that the expression in (i) is algebraically equivalent to 11aaaaaa 2aa 2, which is indeed a binomial. Is she right about the remaining four expressions? Explain your thinking. i. 5aaaaaa 2aa 2 + 6aaaaaa ii. 5xx 3 2xx 2 10xx 4 + 3xx 5 + 3xx ( 2)xx 4 iii. (tt + 2) 2 4tt iv. 5(aa 1) 10(aa 1) + 100(aa 1) v. (2ππππ ππππ 2 )ππ (2ππππ ππππ 2 ) 2ππ S.71
6 3. Suppose Janie writes a polynomial expression using only one variable, xx, with degree of 5, and Max writes a polynomial expression using only one variable, xx, with degree of 5. A. What can you determine about the degree of the sum of Janie s and Max s polynomials? B. What can you determine about the degree of the difference of Janie s and Max s polynomials? 4. Find each sum or difference. A. (2pp + 4) + 5(pp 1) (pp + 7) F. (12xx + 1) + 2(xx 4) (xx 15) B. (7xx 4 + 9xx) 2(xx ) G. (13xx 2 + 5xx) 2(xx 2 + 1) C. (6 tt tt 4 ) + (9tt + tt 4 ) H. (9 tt tt 2 ) 3 2 (8tt + 2tt2 ) D. (5 tt 2 ) + 6(tt 2 8) (tt ) I. (4mm + 6) 12(mm 3) + (mm + 2) E. (8xx 3 + 5xx) 3(xx 3 + 2) J. (15xx xx) 12(xx 4 + 4xx) S.72
Lesson 5: The Distributive Property
Exploratory Exercise Kim was working on an exercise in math when she ran across this problem. Distribute and simplify if possible. (3x + 5) Kim s dad said, I remember doing something like this in school.
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 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 informationLesson 2: Introduction to Variables
Lesson 2: Introduction to Variables Topics and Objectives: Evaluating Algebraic Expressions Some Vocabulary o Variable o Term o Coefficient o Constant o Factor Like Terms o Identifying Like Terms o Combining
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 informationLesson 3: Solving Equations A Balancing Act
Opening Exercise Let s look back at the puzzle in Lesson 1 with the t-shape and the 100-chart. Jennie came up with a sum of 380 and through the lesson we found that the expression to represent the sum
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 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 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 informationCombining Like Terms in Polynomials
Section 1 6: Combining Like Terms in Polynomials Polynomials A polynomial is an expression that has two or more terms each separated by a + or sign. If the expression has only one term it is called a monomial.
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 informationMathB65 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 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 informationUnit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating
Hart Interactive Math Algebra 1 MODULE 2 An algebraic expression that can contains 1 Algebraic Expression variables, numbers and operators (like +,, x and ). 1 Equation An equation is a math sentence stating
More informationUnit 2: Polynomials Guided Notes
Unit 2: Polynomials Guided Notes Name Period **If found, please return to Mrs. Brandley s room, M-8.** 1 Self-Assessment The following are the concepts you should know by the end of Unit 1. Periodically
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 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 informationLesson 12: Solving Equations
Exploratory Exercises 1. Alonzo was correct when he said the following equations had the same solution set. Discuss with your partner why Alonzo was correct. (xx 1)(xx + 3) = 17 + xx (xx 1)(xx + 3) = xx
More informationControlling the Population
Lesson.1 Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term. 1. polynomial a. a polynomial with only 1
More informationI CAN classify polynomials by degree and by the number of terms.
13-1 Polynomials I CAN classify polynomials by degree and by the number of terms. 13-1 Polynomials Insert Lesson Title Here Vocabulary monomial polynomial binomial trinomial degree of a polynomial 13-1
More informationLesson 18: Recognizing Equations of Circles
Student Outcomes Students complete the square in order to write the equation of a circle in center-radius form. Students recognize when a quadratic in xx and yy is the equation for a circle. Lesson Notes
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 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 informationSection 7.1 Quadratic Equations
Section 7.1 Quadratic Equations INTRODUCTION In Chapter 2 you learned about solving linear equations. In each of those, the highest power of any variable was 1. We will now take a look at solving quadratic
More informationCommon Core Standards Addressed in this Resource
Common Core Standards Addressed in this Resource.EE.3 - Apply the properties of operations to generate equivalent expressions. Activity page: 4 7.RP.3 - Use proportional relationships to solve multistep
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 informationSolving Quadratic Equations
Solving Quadratic Equations MATH 101 College Algebra J. Robert Buchanan Department of Mathematics Summer 2012 Objectives In this lesson we will learn to: solve quadratic equations by factoring, solve quadratic
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 Larger and Smaller Numbers................ Practice Actual
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 Pre-Unit Review PS (1 ) Thurs. Sept. Working with Exponents Start Exponent Laws P.S.
More informationMULTIPLYING POLYNOMIALS. The student is expected to multiply polynomials of degree one and degree two.
MULTIPLYING POLYNOMIALS A.10B The student is expected to multiply polynomials of degree one and degree two. TELL ME MORE A polynomial is an expression that is a sum of several terms. Polynomials may contain
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 informationA polynomial is an algebraic expression that has many terms connected by only the operations of +, -, and of variables.
A polynomial is an algebraic expression that has many terms connected by only the operations of +, -, and of variables. 2x + 5 5 x 7x +19 5x 2-7x + 19 x 2 1 x + 2 2x 3 y 4 z x + 2 2x The terms are the
More informationMaintaining Mathematical Proficiency
Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t 4 3. 8s 4 + 4s 6 5s 4. 9m + 3 + m 3 + 5m 5. 4 3p 7 3p 4 1 z 1 + 4 6. ( ) 7. 6( x + ) 4 8. 3( h + 4) 3( h
More informationLesson 14: Solving Inequalities
Hart Interactive Algebra 1 Lesson 14 Classwork 1. Consider the inequality xx 2 + 4xx 5. a. Think about some possible values to assign to xx that make this inequality a true statement. Find at least two
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 informationLESSON #1: VARIABLES, TERMS, AND EXPRESSIONS COMMON CORE ALGEBRA II
1 LESSON #1: VARIABLES, TERMS, AND EXPRESSIONS COMMON CORE ALGEBRA II Mathematics has developed a language all to itself in order to clarify concepts and remove ambiguity from the analysis of problems.
More informationVARIABLES, TERMS, AND EXPRESSIONS COMMON CORE ALGEBRA II
Name: Date: VARIABLES, TERMS, AND EXPRESSIONS COMMON CORE ALGEBRA II Mathematics has developed a language all to itself in order to clarify concepts and remove ambiguity from the analysis of problems.
More informationLESSON 7.2 FACTORING POLYNOMIALS II
LESSON 7.2 FACTORING POLYNOMIALS II LESSON 7.2 FACTORING POLYNOMIALS II 305 OVERVIEW Here s what you ll learn in this lesson: Trinomials I a. Factoring trinomials of the form x 2 + bx + c; x 2 + bxy +
More informationPolynomials. This booklet belongs to: Period
HW Mark: 10 9 8 7 6 RE-Submit Polynomials This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. REVIEW TEST Your teacher
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 information20A. Build. Build and add. Build a rectangle and find the area (product). l e s s o n p r a c t i c e 1. X X X 2 + 6X X
l e s s o n p r a c t i c e 0A Build.. X X. X 6X 8 3. X 8 Build and add. 4. X 6X 3 3X 7X 9 5. X 8 X 6X 7 6. X 0X 7 X 8X 9 Build a rectangle and find the area (product). 7. (X )(X ) = 8. (X 4)(X 3) = 9.
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 informationTeacher Road Map for Lesson 10: True and False Equations
Teacher Road Map for Objective in Student Friendly Language: Today I am: sorting equation cards So that I can: determine when an equation is true or false. I ll know I have it when I can: write my own
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 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 informationName: Chapter 7: Exponents and Polynomials
Name: Chapter 7: Exponents and Polynomials 7-1: Integer Exponents Objectives: Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. You
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 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 information5.2 Polynomial Operations
5.2 Polynomial Operations At times we ll need to perform operations with polynomials. At this level we ll just be adding, subtracting, or multiplying polynomials. Dividing polynomials will happen in future
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 informationMath 3 Variable Manipulation Part 3 Polynomials A
Math 3 Variable Manipulation Part 3 Polynomials A 1 MATH 1 & 2 REVIEW: VOCABULARY Constant: A term that does not have a variable is called a constant. Example: the number 5 is a constant because it does
More informationSection 3.5: Multiplying Polynomials
Section 3.5: Multiplying Polynomials Objective: Multiply polynomials. Multiplying polynomials can take several dierent forms based on what we are multiplying. We will rst look at multiplying monomials;
More informationPolynomials and Polynomial Equations
Polynomials and Polynomial Equations A Polynomial is any expression that has constants, variables and exponents, and can be combined using addition, subtraction, multiplication and division, but: no division
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 informationMath 10-C Polynomials Concept Sheets
Math 10-C 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 informationA-2. Polynomials and Factoring. Section A-2 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 informationUnit 1 Notes. Polynomials
Unit 1 Notes 1 Day Number Date Topic Problem Set 1 Tues. Feb. Operations with Signed Numbers Algebra with Pizzazz Worksheet Wed. Feb. 8 Order of Operations Algebra with Pizzazz Worksheet Thurs. Feb. 9
More informationStudent Instruction Sheet: Unit 1 Lesson 3. Polynomials
Student Instruction Sheet: Unit 1 Lesson 3 Suggested time: 150 min Polynomials What s important in this lesson: You will use algebra tiles to learn how to add/subtract polynomials. Problems are provided
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 informationExponents. Reteach. Write each expression in exponential form (0.4)
9-1 Exponents You can write a number in exponential form to show repeated multiplication. A number written in exponential form has a base and an exponent. The exponent tells you how many times a number,
More informationMath Lecture 18 Notes
Math 1010 - Lecture 18 Notes Dylan Zwick Fall 2009 In our last lecture we talked about how we can add, subtract, and multiply polynomials, and we figured out that, basically, if you can add, subtract,
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 informationLesson 11: Using the Zero Product Property to Find Horizontal Intercepts
: Using the Zero Product Property to Find Horizontal Intercepts Opening Discussion 1. A. Jenna said the product of two numbers is 20. Would the factors have to be 4 and 5? Why? B. Julie said the product
More informationChapter 5: Exponents and Polynomials
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
More informationIn July: Complete the Unit 01- Algebraic Essentials Video packet (print template or take notes on loose leaf)
Hello Advanced Algebra Students In July: Complete the Unit 01- Algebraic Essentials Video packet (print template or take notes on loose leaf) The link to the video is here: https://www.youtube.com/watch?v=yxy4tamxxro
More information1Add and subtract 2Multiply radical
Then You simplified radical expressions. (Lesson 10-2) Now 1Add and subtract radical expressions. 2Multiply radical expressions. Operations with Radical Expressions Why? Conchita is going to run in her
More informationLesson 8: Absolute Value Equations
Warm-Up Exercise 1. Watch the absolute value video on YouTube Math Shorts Episode 10 and then answer the questions below. https://www.youtube.com/watch?v=wrof6dw63es A. 1.3 = B. 4.75 = C. 10 + 4 = D. 11
More informationACTIVITY: Classifying Polynomials Using Algebra Tiles
7. Polynomials classify polynomials? How can you use algebra tiles to model and ACTIVITY: Meaning of Prefixes Work with a partner. Think of a word that uses one of the prefixes with one of the base words.
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 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 informationLESSON 6.2 POLYNOMIAL OPERATIONS I
LESSON 6. POLYNOMIAL OPERATIONS I LESSON 6. POLYNOMIALS OPERATIONS I 63 OVERVIEW Here's what you'll learn in this lesson: Adding and Subtracting a. Definition of polynomial, term, and coefficient b. Evaluating
More informationFunctions: Polynomial, Rational, Exponential
Functions: Polynomial, Rational, Exponential MATH 151 Calculus for Management J. Robert Buchanan Department of Mathematics Spring 2014 Objectives In this lesson we will learn to: identify polynomial expressions,
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 informationLESSON 7.1 FACTORING POLYNOMIALS I
LESSON 7.1 FACTORING POLYNOMIALS I LESSON 7.1 FACTORING POLYNOMIALS I 293 OVERVIEW Here s what you ll learn in this lesson: Greatest Common Factor a. Finding the greatest common factor (GCF) of a set of
More informationAlgebra I Polynomials
Slide 1 / 217 Slide 2 / 217 Algebra I Polynomials 2014-04-24 www.njctl.org Slide 3 / 217 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying
More informationFactoring Polynomials Using the GCF
7.6 Factoring Polynomials Using the GCF polynomial in factored form? How can you use common factors to write a 1 ACTIVITY: Finding Monomial Factors Work with a partner. Six different algebra tiles are
More informationLT1: Adding and Subtracting Polynomials. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms.
LT1: Adding and Subtracting Polynomials *When adding polynomials, simply combine like terms. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms. 1.
More informationPolynomial one or more monomials added or subtracted. (i.e. : 5x or 6xy-3 or 6xy - 5x + 3 or
Polynomials Necessary Terms for Success Welcome back! We will now tackle the world of polynomials. Before we get started with performing operations or using polynomials for applications, we will need some
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 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 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 informationLESSON 6.2 POLYNOMIAL OPERATIONS I
LESSON 6.2 POLYNOMIAL OPERATIONS I Overview In business, people use algebra everyday to find unknown quantities. For example, a manufacturer may use algebra to determine a product s selling price in order
More informationAlgebra Summer Review Packet
Name: Algebra Summer Review Packet About Algebra 1: Algebra 1 teaches students to think, reason, and communicate mathematically. Students use variables to determine solutions to real world problems. Skills
More informationChapter 6: Polynomials
Chapter : Polynomials Chapter : Polynomials POLYNOMIALS Definition: A polynomial is an algebraic epression that is a sum of terms, where each term contains only variables with whole number eponents and
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 informationMath 2 Variable Manipulation Part 3 Polynomials A
Math 2 Variable Manipulation Part 3 Polynomials A 1 MATH 1 REVIEW: 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
More informationP.1: Algebraic Expressions, Mathematical Models, and Real Numbers
Chapter P Prerequisites: Fundamental Concepts of Algebra Pre-calculus notes Date: P.1: Algebraic Expressions, Mathematical Models, and Real Numbers Algebraic expression: a combination of variables and
More informationLesson 7: Lesson Summary. Sample Solution. Write a mathematical proof of the algebraic equivalence of ( ) and ( ). ( ) = ( )
Sample Solution Write a mathematical proof of the algebraic equivalence of () and (). () = () associative property = () commutative property Lesson Summary Properties of Arithmetic THE COMMUTATIVE PROPERTY
More information5-1 Study Guide and Intervention
5-1 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 informationWelcome to Math Video Lessons. Stanley Ocken. Department of Mathematics The City College of New York Fall 2013
Welcome to Math 19500 Video Lessons Prof. Department of Mathematics The City College of New York Fall 2013 An important feature of the following Beamer slide presentations is that you, the reader, move
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 informationPolynomial Operations
Chapter 7 Polynomial Operations Sec. 1 Polynomials; Add/Subtract Polynomials sounds tough enough. But, if you look at it close enough you ll notice that students have worked with polynomial expressions
More informationDON ROBERT B. ESTRELLA SR. NATIONAL HIGH SCHOOL Nagsaag, San Manuel, Pangasinan. (Effective Alternative Secondary Education) MATHEMATICS II
DON ROBERT B. ESTRELLA SR. NATIONAL HIGH SCHOOL Nagsaag, San Manuel, Pangasinan. (Effective Alternative Secondary Education) MATHEMATICS II Y X MODULE 1 Quadratic Equations BUREAU OF SECONDARY EDUCATION
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 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 informationWhat is a constant? A Constant is a number representing a quantity or value that does not change.
Worksheet -: Algebraic Expressions What is a constant? A Constant is a number representing a quantity or value that does not change. What is a variable? A variable is a letter or symbol representing a
More informationProperties of Real Numbers
Pre-Algebra Properties of Real Numbers Identity Properties Addition: Multiplication: Commutative Properties Addition: Multiplication: Associative Properties Inverse Properties Distributive Properties Properties
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 information2, or x 5, 3 x 0, x 2
Pre-AP Algebra 2 Lesson 2 End Behavior and Polynomial Inequalities Objectives: Students will be able to: use a number line model to sketch polynomials that have repeated roots. use a number line model
More informationAlgebra Workbook WALCH PUBLISHING
Algebra Workbook WALCH PUBLISHING Table of Contents Unit 1: Algebra Basics Activity 1 What Are Negative and Positive Numbers? I...1 Activity 2 What Are Negative and Positive Numbers? II..2 Activity 3 Larger
More information