Unit 13: Polynomials and Exponents
|
|
|
- Clarence Simmons
- 6 years ago
- Views:
Transcription
1 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: Division Properties of Exponents KEY TERMS AND CONCEPTS Look for the following terms and concepts as you work through the Media Lesson. In the space below, explain the meaning of each of these concepts and terms in your own words. Provide examples that are not identical to those in the Media Lesson. Polynomial Monomial Binomial Trinomial Leading Term
2 Leading Coefficient Degree of a Polynomial Constant Term The Multiplication Property Raising a Power to a Power Raising a Product to a power The Division Property Raising a Quotient to a Power
3 Unit 13: Media Lesson Section 13.1: Polynomials Definitions Polynomial: An algebraic expression composed of the sum of terms containing a single variable raised to a non-negative integer exponent. Monomial: A polynomial consisting of one term Binomial: A polynomial consisting of two terms Trinomial: A polynomial consisting of three terms Leading Term: The term that contains the highest power of the variable in a polynomial Leading Coefficient: The coefficient of the leading term Constant Term: A number with no variable factors. A term whose value never changes. Degree: The highest exponent in a polynomial Example 1: Complete the table. Polynomial Name Leading Coefficient Constant Term Degree a a m m 2m 8 5x 2 + x 3 7 2x + 4 4x 3
4 Media Lesson Section 13.1 You Try Complete the table. Polynomial Name Leading Coefficient Constant Term Degree n² 2n + 8 4x 3 6x 7
5 Media Lesson Section 13.2: Operations on Polynomials Addition of Polynomials Example 1: Add. (3n 2 2n + 8) + (3n 3 7n 2 n 9) Subtraction of Polynomials Example 2: Subtract. (a 3 + 5a + 11) (4a 3 + 6a 2 a + 1) Combine and Simplify Example 3: Perform the indicated operations. Simplify. (3x 1) (x 2 x 9) + (4x 3 + x 2 7x + 2)
6 Media Lesson Section 13.2 YOU TRY Perform the indicated operations. Simplify completely. Show all steps as in the media examples. a. (x 2 x + 8) + (5x 2 6x 11) b. (8x 2 4x + 5) (3x 2 4x + 6) c. (5x + 8) + (x 2 x 1) (x 3 + 3x 2 4x + 8)
7 Media Lesson Section 13.3: Properties of Exponents Given any real numbers a, b, c, m, and n n 1 = 1 n = n 0 = 0 n = n 0 n = Multiplication Properties of Exponents 3 3 = a m a n = a m+n 3 2 = Why? 3 1 = (a m ) n = a mn Why? 3 0 = 3-1 = 3-2 = 3-3 = 3-4 = Example 1: Evaluate and simplify the following expressions. Assume x 0, x -1/2, a 0, b 0, and c 0. 5x 0 (2x + 1) 0 a 0 + b 0 + c 0 The Multiplication Property: a m a n = a m+n Example 2: Simplify the following expressions n 3 n 9 b 5 b 4 b 5x 2 y 5 (7xy 9 )
8 Media Lesson Raising a Power to a Power: (a m ) n = a mn Example 3: Simplify the following expressions (x 3 ) 9 5b 2 (b 5 ) 8 Raising a Product to a Power: (ab) n = a n b n Example 4: Simplify the following expressions (5x) 2 (x 3 y 2 ) 9 ( 8ab 5 ) 2 5( 2w 7 ) 3 5n 4 ( 3n 3 ) 2 Section 13.3 You Try Simplify the following expressions. Show all steps as in the media examples. a. (2x 4 ) 2 b. 2(x 2 ) 3 c. 8g 3 5g 4 d. 2n 0
9 Media Lesson Section 13.4: Multiplication of Polynomials Multiplication of Monomials Example 1: Multiply and simplify. (3x 5 )( 2x 9 ) Example 2: Expand and simplify. The Distributive Property 5x 3 (2x 5 4x 3 x + 8) Example 3: Multiply and simplify. a. (x + 3)(x + 4) Multiplication of Polynomials b. (m 5)(m 6) c. (2d 4)(3d + 5) d. (x 2)(x 2 + 2x 4)
10 Media Lesson Example 4: Multiply and simplify Squaring a Binomial a. (n + 5) 2 b. (3 2a) 2 Section 13.4 You Try Multiply and simplify. Show all steps as in the media examples. a. 3x 2 (x 5 + 6x 3 5x) b. (3x 4)(5x + 2) c. (2p 5) 2
11 Media Lesson Section 13.5: Applications from Geometry Example 1: Write a polynomial in simplest form that represents the area of the square. x y x A C y B D Example 1 (another way): Write a polynomial in simplest form that represents the area of the square. x y x A C y B D Example 2: Write a polynomial in simplest form that represents the area of the shaded region.
12 Media Lesson Section 13.5 You Try Write a polynomial in simplest form that represents the area of the dark blue region of the figure shown below. Show all steps as in the media examples. x 2 x 5
13 Media Lesson Section 13.6: Division Properties of Exponents The Division Property: a m a n = am n a 0 x 5 = x x x x x x 2 x x = x x x 1 = x3 1 = x3 x 5 x 2 = x5 2 = x 3 Example 1: Simplify the following expressions. Variables represent nonzero quantities. x 50 4a 10 b 5 x 4 6ab 2 Raising a Quotient to a Power: ( a b )n = an b n b 0 Example 2: Simplify the following expressions. Variables represent nonzero quantities. ( 5 7 )2 ( x5 y 3)4 ( 4t10 u 6 )2
14 Media Lesson Section 13.6 You Try Simplify the following expressions. Variables represent nonzero quantities. Show all steps as in the media examples. a. ( 3a10 7 )2 b. 6x 3 y 8 9xy 5
15 Name: Date: 1. Complete the table below. Unit 13: Practice Problems Skills Practice Polynomial Name Leading Coefficient Constant Term Degree 5n 8 n x 5 8r 2 2. Simplify completely. Show all steps, and box your answers. a. (2x) 3 b. 5(3n) 2 c. y 3 y 7 y d. ( 2x) 3 e. 5w(8w 3 ) f. ( 2x 5 ) 2
16 Practice Problems g. ( 5w 8 ) 2 h. 3x 0 + 2x 0 i. ( 4x) 2 + 4x 2 j. (5x 7) 0 3. Multiply and simplify completely. Show all steps, and box your answers. a. 4x 2 (3x 5) b. 4a 2 (3a 2 2a 5) c. (p + 5)(p + 7) d. (x + 2)(x 2) e. (2x 4)(3x 5) f. (5w 8)(3w + 11)
17 Practice Problems g. (x + 2) 2 h. (2x 4) 2 i. (x 4)(x 2 + x 5) j. 3(x + 2)(x + 4) k. 4(x + 2) 2 l. (q 2) 3 4. Simplify completely. Show all steps, and box your answers. a. x8 x 3 b. (2 5 )4 c. 8n8 p 5 12np 4 d. (3a5 7b )2
18 Practice Problems 5. Evaluate the algebraic expression x 2 given x = 7. Show your work. 6. Evaluate the algebraic expression 5x 3 given x = 2. Show your work. 7. Evaluate the algebraic expression (5x) 2 given x = 2. Show your work. 8. Evaluate the algebraic expression 5(2x) 2 given x = 3. Show your work. 9. Evaluate the algebraic expression 6 5x given x = 2. Show your work. 10. Evaluate the algebraic expression 1 4x2 given x = 5. Show your work.
19 Practice Problems Applications 11. Write an algebraic expression that represents the perimeter of the figure shown below. Simplify completely. Show your work. 5x 4 x Write an algebraic expression that represents the total area of the figure shown below. Simplify completely. Show your work. 5x 4 x Write an expression that represents the total are of the figure shown below. Simplify completely. 14. Write an expression that represents the area of the shaded region of the figure shown below. Simplify completely.
20 Practice Problems 15. Write an expression that represents the total area of the figure shown below. Simplify completely. a b a b a b 16. Write an expression that represents the perimeter of the figure shown below. Simplify completely. a b a b a b 17. Write an algebraic expression that represents the total area of the figure shown below. Simplify completely. Show your work. 6x x 6x x 6x x
21 Practice Problems Extension 18. If possible, simplify each of the following by combining like terms or using properties of exponents. a. 2n 5 + 3n 5 = b. 2n 5 3n 5 = c. 3n 3 + 3n 5 = d. 3n 3 3n 5 = 19. Write an algebraic expression that represents the total area of the figure shown below. Simplify completely. Show your work. 20. Write a polynomial in simplest form that represents the volume of the figure shown below.
22 Practice Problems 21. Simplify completely. Show all steps, and box your answers. a. 4p( 5p 3 ) 2 b. 3( 2x) 3 3x( 2) 3 c. 4w 5 (3w 8 ) 2 d. 10p 3 ( 5p 7 ) 2 e. 2a 3 b(3ab 5 ) 2 f. (3x 4 ) 3 (5x 6 ) 2
23 Name: Date: Unit 13: Review 1. Consider the polynomial n 2 7n 11 a. Is this a monomial, binomial, or trinomial? b. Identify the constant term. c. What is the leading coefficient? d. What is the degree of this polynomial? e. Identify the coefficient of the second term. 2. If possible, simplify each of the following by combining like terms or using properties of exponents. a. 8n 3 + 5n 3 = b. 8n 3 5n 3 = c. 8n 3 + 8n 5 = d. 8n 3 8n 5 = 3. Simplify completely. Show all steps, and box your answers. a. ( 5x 5 ) 3 b. 4x 2 (8x 2 5x 3) c. (3 5x) 2 d. 24m 8 18m 3 e. ( 5x 3 )2 f. (4x 3 + 6x 2 x + 7) (3x 3 + x 2 x 5)
24 Review 4. Evaluate the algebraic expression 8(2x) 2 given x = 5. Show your work Evaluate the algebraic expression 2 3x given x = 4. Show your work. 6. Write an algebraic expression that represents the perimeter of the figure shown below. Simplify completely. Show your work. 4x 2 x Write an algebraic expression that represents the total area of the figure shown below. Simplify completely. Show your work. 4x 2 x + 8
25
Lesson 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
Something 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
Chapter 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
Lesson 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
Lesson 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
Never 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
I 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
Lesson 2 - Mini-Lesson. Section 2.1 Properties of Exponents
Lesson - Mini-Lesson Section.1 Properties of Exponents What is an exponent? An exponent is a number in the superscript location and identifies the number of times the base number is to be multiplied times
Properties of Real Numbers
Pre-Algebra Properties of Real Numbers Identity Properties Addition: Multiplication: Commutative Properties Addition: Multiplication: Associative Properties Inverse Properties Distributive Properties Properties
5.2. 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.
Accuplacer 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
Polynomials 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,
Unit 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
TABLE 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
CHAPTER 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)
Name: 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
Algebra. 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
Collecting Like Terms
MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.
Ready To Go On? Skills Intervention 7-1 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 7-1 Integer Exponents Negative Exponent:
Section 5.2 Polynomials, Sums, and Differences
Department of Mathematics Grossmont College October 2, 2012 4.1 Systems of Linear Equations in Two Variables Learning Objectives: Give the degree of a polynomial Add and subract polynomials evaluate a
Unit 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
A-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
Unit 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
Unit 1 Vocabulary. A function that contains 1 or more or terms. The variables may be to any non-negative power.
MODULE 1 1 Polynomial A function that contains 1 or more or terms. The variables may be to any non-negative power. 1 Modeling Mathematical modeling is the process of using, and to represent real world
Review 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
Unit 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.
5.1 Monomials. Algebra 2
. Monomials Algebra Goal : A..: Add, subtract, multiply, and simplify polynomials and rational expressions (e.g., multiply (x ) ( x + ); simplify 9x x. x Goal : Write numbers in scientific notation. Scientific
Math 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
MATHEMATICS 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
{ 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
AFM Review Test Review
Name: Class: Date: AFM Review Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. What are the solutions of the inequality?. q + (q ) > 0 q < 3 q
Unit 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
Polynomials 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
Exponents and Polynomials. (5) Page 459 #15 43 Second Column; Page 466 #6 30 Fourth Column
Algebra Name: Date: Period: # Exponents and Polynomials (1) Page 453 #22 59 Left (2) Page 453 #25 62 Right (3) Page 459 #5 29 Odd (4) Page 459 #14 42 First Column; Page 466 #3 27 First Column (5) Page
6.1 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.
Algebra 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 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02
Day 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
Chapter 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
Chapter 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
We 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)
Algebra Review. Terrametra Resources. Lynn Patten
Terrametra Resources Lynn Patten ALGEBRAIC EXPRESSION A combination of ordinary numbers, letter symbols, variables, grouping symbols and operation symbols. Numbers remain fixed in value and are referred
FastTrack - 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
5-1 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
Controlling 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
Mathwithsheppard.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
Algebra 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
Sections 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
20A. 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.
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
Example #3: 14 (5 + 2) 6 = = then add = 1 x (-3) then. = 1.5 = add
Grade 9 Curricular content Operations with rational numbers (addition, subtraction, multiplication, division and order of operations) -incudes brackets and exponents (exponent laws) -exponents includes
Math 154 :: Elementary Algebra
Math :: Elementar Algebra Section. Section. Section. Section. Section. Section. Math :: Elementar Algebra Section. Eponents. When multipling like-bases, ou can add the eponents to simplif the epression..
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.
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
What 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
Polynomials: 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
1.3 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
Combining 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.
Beginning 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:
LESSON 6.1 EXPONENTS LESSON 6.1 EXPONENTS 253
LESSON 6.1 EXPONENTS LESSON 6.1 EXPONENTS 5 OVERVIEW Here's what you'll learn in this lesson: Properties of Exponents Definition of exponent, power, and base b. Multiplication Property c. Division Property
Ex.1 identify the terms and coefficients of the expression.
Modeling with expressions An expression is a mathematical phrase that contains numbers or variables. Terms are the parts being added. Coefficient is the number in front of the variable. A constant is a
Solving Equations Quick Reference
Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number
Polynomial 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
review 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
A 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
POLYNOMIAL: 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 NON-EXAMPLES: Variable as an exponent A sum x x 3 The product of variables 5a The product of numbers
Student 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
Chapter 5 Rational Expressions
Worksheet 4 (5.1 Chapter 5 Rational Expressions 5.1 Simplifying Rational Expressions Summary 1: Definitions and General Properties of Rational Numbers and Rational Expressions A rational number can be
Degree of a polynomial
Variable Algebra Term Polynomial Monomial Binomial Trinomial Degree of a term Degree of a polynomial Linear A generalization of arithmetic. Letters called variables are used to denote numbers, which are
P.1 Prerequisite skills Basic Algebra Skills
P.1 Prerequisite skills Basic Algebra Skills Topics: Evaluate an algebraic expression for given values of variables Combine like terms/simplify algebraic expressions Solve equations for a specified variable
27 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
Mathematics Textbook Correlation to the 2016 Algebra I Standards of Learning and Curriculum Framework
and Curriculum Framework Publisher: McGraw-Hill School Education Text: Algebra 1 Copyright date 2018 A.1 The student will a) represent verbal quantitative situations algebraically; and TE: 5-9, 23-29,
How could you express algebraically, the total amount of money he earned for the three days?
UNIT 4 POLYNOMIALS Math 11 Unit 4 Introduction p. 1 of 1 A. Algebraic Skills Unit 4 Polynomials Introduction Problem: Derrek has a part time job changing tires. He gets paid the same amount for each tire
Algebraic Expressions and Identities
9 Algebraic Epressions and Identities introduction In previous classes, you have studied the fundamental concepts of algebra, algebraic epressions and their addition and subtraction. In this chapter, we
Understand 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
Due for this week. Slide 2. Copyright 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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 6.1-6.4, Do the MyMathLab Self-Check for week 1. Learning team coordination/connections.
Section 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
Beginning Algebra. 1. Review of Pre-Algebra 1.1 Review of Integers 1.2 Review of Fractions
1. Review of Pre-Algebra 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:
MATH98 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)
5.1 Modelling Polynomials
5.1 Modelling Polynomials FOCUS Model, write, and classify polynomials. In arithmetic, we use Base Ten Blocks to model whole numbers. How would you model the number 234? In algebra, we use algebra tiles
Northwood High School Algebra 2/Honors Algebra 2 Summer Review Packet
Northwood High School Algebra 2/Honors Algebra 2 Summer Review Packet This assignment should serve as a review of the Algebra 1 skills necessary for success. Our hope is that this review will keep your
NAME 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
Unit 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
MathB65 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
How 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
Intensive Math-Algebra I Mini-Lesson MA.912.A.4.3
Intensive Math-Algebra I Mini-Lesson M912.4.3 Summer 2013 Factoring Polynomials Student Packet Day 15 Name: Date: Benchmark M912.4.3 Factor polynomials expressions This benchmark will be assessed using
POLYNOMIAL 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
x y x y ax bx c x Algebra I Course Standards Gap 1 Gap 2 Comments a. Set up and solve problems following the correct order of operations (including proportions, percent, and absolute value) with rational
ASSIGNMENT. Please complete only the assignment for the class you will begin in September 2018.
ASSIGNMENT Attached is an assignment containing items necessary for you to have mastered to do well in Algebra II. Please complete only the assignment for the class you will begin in September 2018. Practicing
MATH 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: 1-75 odd) A. Simplify fractions. B. Change mixed numbers
LESSON 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
LESSON 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
Math "Adding and Subtracting Polynomials" Bibiana Lopez. July Riverside City College. (RCC) 10.1 July / 15
Math 64 10.1 "Adding and Subtracting Polynomials" Bibiana Lopez Riverside City College July 2010 (RCC) 10.1 July 2010 1 / 15 Objectives: * Add and subtract polynomials. * Evaluate polynomials at given
Introduction. Adding and Subtracting Polynomials
Introduction Polynomials can be added and subtracted like real numbers. Adding and subtracting polynomials is a way to simplify expressions. It can also allow us to find a shorter way to represent a sum
Algebra. Table of Contents
Algebra...4 Patterns...5 Adding Real Numbers...7 Subtracting Real Numbers...9 Multiplying Real Numbers...11 Dividing Real Numbers...12 Order of Operations...13 Real-Number Operations with Absolute Value...16
Solving 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
Algebra 31 Summer Work Packet Review and Study Guide
Algebra Summer Work Packet Review and Study Guide This study guide is designed to accompany the Algebra Summer Work Packet. Its purpose is to offer a review of the ten specific concepts covered in the
Math 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
Algebra 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
Algebra 2 (3) Apex - Semester 1 Part A
Algebra 2 (3) Apex - Semester 1 Part A Name Algebra I Literacy Advantage Unit 1 : The Need to Read Lesson 1.1 : Reading and Vocabulary Activity 1.1.1 : Study - Active Reading Learn skills and strategies
Algebra I. Polynomials.
1 Algebra I Polynomials 2015 11 02 www.njctl.org 2 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying a Polynomial by a Monomial Multiplying
LESSON 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