Lesson 3: Polynomials and Exponents, Part 1
|
|
- Liliana Chambers
- 5 years ago
- Views:
Transcription
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 in depth at variables with exponents and how to work with them. We then look at polynomials that contain variables with exponents. Section 3.1: Polynomials Section 3.2: Operations on Polynomials Section 3.3: Properties of Exponents Section 3.4: Multiplication of Polynomials Section 3.5: Applications from Geometry Scottsdale Community College Page 43 Introductory Algebra
2 Lesson 3 Checklist Component Required? Y or N Comments Due Score Online Homework Online Quiz Online Test Practice Problems Lesson Assessment Scottsdale Community College Page 44 Introductory Algebra
3 Name: Date: 3 Section 3.1: Polynomials Definitions Polynomial: An algebraic expression composed of the sum of terms containing a single variable raised to a positive 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. 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 Scottsdale Community College Page 45 Introductory Algebra
4 You Try 1. Complete the table. Polynomial Name Leading Coefficient Constant Term Degree 3n 2! 2n +8 4x x 2! 7 Scottsdale Community College Page 46 Introductory Algebra
5 Section 3.2: 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) 2. Perform the indicated operations. Simplify. You Try ( 5x +8) + ( 3x 2! 4x!1)! ( 5x 3 + 3x 2! 4x + 6) Scottsdale Community College Page 47 Introductory Algebra
6 Scottsdale Community College Page 48 Introductory Algebra
7 Section 3.3: Properties of Exponents Given any real numbers a, b, c, m, and n n 1 = 1 n = n 0 = 0 n = n! 0 n! 0 Example 1: Evaluate and simplify the following expressions. Assume x 0, x -1/2, a 0, b 0, and c 0. a. 5x 0 b. ( 2x +1) 0 c. a 0 + b 0 + c 0 The Multiplication Property: a m a n = a m+ n Example 2: Simplify the following expressions. a. n 3 n 9 b. b 5! b 4! b c. 5x 2 y 5 ( 7xy 9 ) Raising a Power to a Power: ( m n mn a ) = a Example 3: Simplify the following expressions. a. ( x 3 ) 9 b. 5b 2 ( b 5 ) 8 Scottsdale Community College Page 49 Introductory Algebra
8 Raising a Product to a Power: ( n n ab ) = a b n Example 4: Simplify the following expressions. a. ( 5x) 2 b. ( x 3 y 2 ) 9 c. (!8ab 5 ) 2 d. 5 (!2w 7 ) 3 e. 5n 4 (!3n 3 ) 2 3. Simplify the following expressions. You Try a. 3 (!2x 4 ) 2 b. 2x (!3x 2 ) 3 c. g 3! g 4! g 5 d. 2n 0 Scottsdale Community College Page 50 Introductory Algebra
9 Section 3.4: 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) Scottsdale Community College Page 51 Introductory Algebra
10 Example 4: Multiply and simplify. Squaring a Binomial a. ( n + 5) 2 b. ( 3! 2a) 2 4. Multiply and simplify. You Try a.!3x 2 ( x 5 + 6x 3! 5x) b. ( 3x! 4) ( 5x + 2) c. ( 2p! 5) 2 Scottsdale Community College Page 52 Introductory Algebra
11 Section 3.5: Applications from Geometry Example 1: Write a polynomial in simplest form that represents the area of the square. SOLUTION: x y x A C y B D Region A has area: x! x = x 2 Regions B and C each have area: x! y = xy Region D has area: y! y = y 2 Total Area = x 2 + xy + xy + y 2 = y 2 + x 2 + 2xy Example 1 (another way): Write a polynomial in simplest form that represents the area of the square. SOLUTION: x y x A C y B D The total length of each side is x + y. Total Area = ( x + y) ( x + y) = x 2 + xy + yx + y 2 Note that xy and yx are like terms: xy + yx = 2xy Total Area = x 2 + 2xy + y 2 Example 2: Write a polynomial in simplest form that represents the area of the shaded region. SOLUTION: To find the area of the shaded region we find the area of the big square and subtract the area of the little square. The big square has area: y! y = y 2 Each little square has area: x! x = x 2 Area of the shaded region = y 2! 4x 2 Scottsdale Community College Page 53 Introductory Algebra
12 You Try 5. Write a polynomial in simplest form that represents the total area of the figure shown below. x x Write a polynomial in simplest form that represents the area of the dark blue region of the figure shown below. x x 2 5 Scottsdale Community College Page 54 Introductory Algebra
Unit 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 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 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 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 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 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 informationLesson 5: Solving Equations
Up to this point, our study of algebra has involved a deep look at algebraic expressions and operations on those expressions. We ve learned how to characterize, write, and simplify algebraic expressions,
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 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 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 6b Rational Exponents & Radical Functions
Lesson 6b Rational Exponents & Radical Functions In this lesson, we will continue our review of Properties of Exponents and will learn some new properties including those dealing with Rational and Radical
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 informationCollecting 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.
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 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 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 informationExponents 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
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 information5.3. 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 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 informationSection 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
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 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 informationAFM 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
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 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 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 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 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 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 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 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 informationAdding and Subtracting Polynomials Add and Subtract Polynomials by doing the following: Combine like terms
POLYNOMIALS AND POLYNOMIAL OPERATIONS STUDY GUIDE Polynomials Polynomials are classified by two different categories: by the number of terms, and the degree of the leading exponent. Number Classification
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 informationMathematics 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,
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 informationIntroduction. 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
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 informationAlgebra I Classroom Guide
SkillsTutor Algebra I Classroom Guide Table of Contents Getting Started... 1 Algebra I Lessons... 2 Quizzes...2 Tests...2 Algebra I Lesson Summaries... 3 Equations, Inequalities, and Polynomials...4 Factoring
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 "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
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 NON-EXAMPLES: Variable as an exponent A sum x x 3 The product of variables 5a The product of numbers
More informationIntensive 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
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 informationOrder of Operations Practice: 1) =
Order of Operations Practice: 1) 24-12 3 + 6 = a) 6 b) 42 c) -6 d) 192 2) 36 + 3 3 (1/9) - 8 (12) = a) 130 b) 171 c) 183 d) 4,764 1 3) Evaluate: 12 2-4 2 ( - ½ ) + 2 (-3) 2 = 4) Evaluate 3y 2 + 8x =, when
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 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 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 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 informationLesson 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
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 informationUnit 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
More informationNorthwood 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
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 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 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 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 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 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 informationReady 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:
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 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 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02
More informationAlgebra 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
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 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 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 informationAlgebra 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
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 informationLesson 5b Solving Quadratic Equations
Lesson 5b Solving Quadratic Equations In this lesson, we will continue our work with Quadratics in this lesson and will learn several methods for solving quadratic equations. The first section will introduce
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 informationAlgebra 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
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 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 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
More informationModule 11 Lesson 3. Polynomial Functions Quiz. Some questions are doubled up if a pool wants to be set up to randomize the questions.
Module 11 Lesson 3 Polynomial Functions Quiz Some questions are doubled up if a pool wants to be set up to randomize the questions. Question 1: Short answer/fill in the blank Find the limit graphically:
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 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 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 informationAlgebraic Expressions
Algebraic Expressions 1. Expressions are formed from variables and constants. 2. Terms are added to form expressions. Terms themselves are formed as product of factors. 3. Expressions that contain exactly
More informationFactoring Trinomials of the Form ax 2 + bx + c, a 1
Factoring Trinomials of the Form ax 2 + bx + c, a 1 When trinomials factor, the resulting terms are binomials. To help establish a procedure for solving these types of equations look at the following patterns.
More informationMath 9 Homework & Notebook
Math 9 Homework & Notebook Name: Block: Teacher: Miss Zukowski Date Submitted: / / 2018 Unit # : Submission Checklist: (make sure you have included all components for full marks) Cover page & Assignment
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 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 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 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 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 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 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 informationAlgebra 2. Factoring Polynomials
Algebra 2 Factoring Polynomials Algebra 2 Bell Ringer Martin-Gay, Developmental Mathematics 2 Algebra 2 Bell Ringer Answer: A Martin-Gay, Developmental Mathematics 3 Daily Learning Target (DLT) Tuesday
More informationMath 10 - Unit 5 Final Review - Polynomials
Class: Date: Math 10 - Unit 5 Final Review - Polynomials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Factor the binomial 44a + 99a 2. a. a(44 + 99a)
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 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 informationLESSON 8.1 RATIONAL EXPRESSIONS I
LESSON 8. RATIONAL EXPRESSIONS I LESSON 8. RATIONAL EXPRESSIONS I 7 OVERVIEW Here is what you'll learn in this lesson: Multiplying and Dividing a. Determining when a rational expression is undefined Almost
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 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 informationSUMMER ASSIGNMENT FOR ALGEBRA II/TRIGONOMETRY
SUMMER ASSIGNMENT FOR ALGEBRA II/TRIGONOMETRY This summer assignment is designed to ensure that you are prepared for Algebra II/ Trigonometry. Nothing on this summer assignment is new. Everything is a
More informationMATH 190 KHAN ACADEMY VIDEOS
MATH 10 KHAN ACADEMY VIDEOS MATTHEW AUTH 11 Order of operations 1 The Real Numbers (11) Example 11 Worked example: Order of operations (PEMDAS) 7 2 + (7 + 3 (5 2)) 4 2 12 Rational + Irrational Example
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 informationAdding and Subtracting Polynomials
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.
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 information