ALGEBRA REVIEW. MULTINOMIAL An algebraic expression consisting of more than one term.
|
|
- Branden Garrison
- 6 years ago
- Views:
Transcription
1 Page 1 of 6 ALGEBRAIC EXPRESSION A cobination of ordinary nubers, letter sybols, variables, grouping sybols and operation sybols. Nubers reain fixed in value and are referred to as constants. Letter sybols represent nubers that are fixed in value, but are unspecified. Variables are letter sybols representing single nubers or sets of nubers. 5 5xy z Exaples: 5, x 6, x 5 6, x 5xy y, a b, a c TERM Consists of products and quotients of ordinary nubers and letters that represent nubers. Grouped sybols are considered as a single nuber. 7 Exaples: 6x y, 5x / y, x x y y 1/ a x,, MONOMIAL An algebraic expression consisting of only one ter. Monoials are soeties siply called ters. Exaples: 7x y, xyz, x / y BINOMIAL An algebraic expression consisting of two ters. Exaples: x y, x xyz TRINOMIAL An algebraic expression consisting of three ters. Exaples: x 5x, x 6y z, x xy / z x z MULTINOMIAL An algebraic expression consisting of ore than one ter. Exaples: 7x 6y, x 6x y 7xy 6, 7x 5x / y x / 16 COEFFICIENT One factor of a ter is said to be the coefficient of the rest of the ter. Exaples: in the ter 5x y, 5x is the coefficient of y, 5y is the coefficient of and 5 is the coefficient of x y The nueric factor of a ter is the nueric coefficient and is often referred to siply as the coefficient. Exaple: in the ter 5x y, 5 is the nueric coefficient. 7 x, Copyright 001
2 Page of 6 LIKE TERMS or SIMILAR TERMS Ters which differ only in nueric coefficients. Exaples: 7 xy and xy are like ters, and 1 x y and x y are like ters. Note: 7 a b and a b are unlike ters. Two or ore like ters in an algebraic expression ay be cobined into one ter. Exaple: 7x y x y x y ay be cobined as 5 x y INTEGRAL and RATIONAL TERMS Ters consisting of a) positive integral powers of literal nubers ultiplied by a factor not containing the letters -orb) no literal nubers at all are integral and rational. 6 Exaples: 6x y, 5y, 7, x, x y are integral and rational in the letters present. Note: x is not rational in x and / x is not integral in x POLYNOMIAL A onoial or ultinoial in which every ter is integral and rational in the literals. Exaples: x y 5x y, x 7x x 5x, xy z, x Note: x / x and y are not polynoials. DEGREE of a MONOMIAL The su of all the exponents in the literal part of the ter. Exaple: the degree of x y z is 1 or 6 Note: the degree of a constant such as 6, 0, and is zero. DEGREE of a POLYNOMIAL The degree of the ter having the highest degree and a non-zero coefficient. 5 Exaple: 7x y xz x y has ters of degree 5, 6, respectively hence, the degree of the polynoial is 6 Copyright 001
3 Page of 6 SYMBOLS of GROUPING Parentheses ( ), brackets [ ], and braces { } are often used to show that the ters contained in the are considered as a single quantity. Exaple: two algebraic expressions 5x x y and x y ay be cobined as a su: 5 x x y x y or a difference: 5 x x y x y or a product: 5 x x y x y REMOVAL of SYMBOLS of GROUPING If a + sign precedes a sybol of grouping, this sybol ay be reoved without affecting the ters contained. Exaple: x 7 y xy x x 7y xy x If a sign precedes a sybol of grouping, this sybol ay be reoved only if the sign of each ter contained is changed. Exaple: x 7 y xy x x 7 y xy x If ore than one sybol of grouping is present, the inner ones are to be reoved first. x x x 5y x x x 5y x x x 5 Exaple: y ADDITION of ALGEBRAIC EXPRESSIONS Achieved by cobining like ters. In order to accoplish this addition, the expressions ay be arranged in rows with like ters in the sae colun; these coluns are then added. Exaple: to add 7x y xy, x y 7xy and xy 5x 6y write: and add 7x y xy x y 7xy 5x 6y xy 5x 5y 5xy SUBTRACTION of ALGEBRAIC EXPRESSIONS Achieved by changing the sign of every ter in the expression that is being subtracted and adding this result to the other expression. Exaple: to subtract x 5xy 5y fro 9x xy y write: and add ( 9x xy y = x 5xy 5y ) = 9x xy y x 5xy 5y 7x xy 8y Copyright 001
4 Page of 6 MULTIPLICATION of ALGEBRAIC EXPRESSIONS To ultiply two or ore onoials, use the laws of exponents, the rules of signs, and the coutative and associative laws of ultiplication. Exaple: to ultiply x y z, x y and xy z write: x y z x y xy z rearrange: x x x y yy z z 7 8 and ultiply x y z To ultiply a polynoial by a onoial, ultiply each ter of the polynoial by the onoial and cobine results. Exaple: to ultiply xy x xy and 5x y write: 5 x y xy x xy distribute: 5 x y xy + 5 x y x + 5 x y xy and ultiply 15x y 0x y 10x y To ultiply a polynoial by a polynoial, ultiply each of the ters of one polynoial by each of the ters of the other polynoial and cobine results. Exaple: to ultiply x 9 x and x x x 9 x write: distribute: x 9 x + x x 9 x ultiply: 9x 7 x + x 9x x and add x 6x 18x 7 DIVISION of ALGEBRAIC EXPRESSIONS To divide a onoial by a onoial, find the quotient of the nueric coefficients, find the quotients of the literal factors, and ultiply these quotients. To divide a polynoial by a polynoial a) Arrange the ters of both polynoials in descending (or ascending) powers of one of the letters coon to both polynoials. b) Divide the first ter in the dividend by the first ter in the divisor. This gives the first ter in the quotient. c) Multiply the first ter of the quotient by the divisor and subtract fro the dividend, thus obtaining a new dividend. d) Use the dividend obtained in c) to repeat steps b) and c) until a reainder is obtained which is either of degree lower than the degree of the divisor or zero. dividend reainder e) The result is written quotient. divisor divisor Copyright 001
5 Page 5 of 6 EXPONENT or POWER An exponent signifies the nuber of ties a nuber is to be ultiplied by itself. Exaple: In the expression x, x is the base and is the exponent. ( This eans x is ultiplied by itself ties or x x x x ) To ultiply when the bases are the sae, add the exponents. n n x x x To divide when the bases are the sae, subtract the exponents. n n x x x A negative exponent can be written as its own reciprocal. x 1/ x and x 1 / x Anything (except zero itself) with a 0 exponent equals 1. x 0 1 when x 0 To raise an exponent to a power, ultiply the exponents. n n x x Exponents are distributive through ultiplication and division. ax a x y y A fractional exponent indicates a root. x 1 x since x x x x x 1 1 Copyright 001
6 Page 6 of 6 EQUATION A stateent of equality between algebraic expressions. Exaple: for the equation x 6, there is a nuber which when substituted for x will resolve the equation to 6 6. That nuber is. The single overall rule to follow in working with equations is that you can do alost anything to an equation as long as the equality is preserved. All of the rules that follow are based on this single rule. Distributive property: (sae as arithetic) ab c ab ac Identical operations on both sides of the equation: Addition: if a b then a c b c Subtraction: if a b then a c b c Multiplication: if a b then a c b c Division: if a b then a / c b / c Siplification: If two ters on the sae side of an equation are identical, except for the algebraic sign (one ter added and the other subtracted), they will cancel each other and can both be eliinated. Additive identity: a b b a b b a 0 a If two ters on the sae side of an equation are identical, one ultiplying and the other dividing that side of the equation, they will cancel each other and can both be eliinated. Multiplicative identity: a b / b a b / b a 1 a Transposition: A ter ay be oved fro one side of the equation to the other by applying the properties stated above. In each of the following equations, the value of x is solved for by isolating it on one side of the equation. Addition: if x a b then x b a Subtraction: if x a b then x b a Multiplication: if x / a b then x b a Division: if x a b then x b / a Copyright 001
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
More informationa a a a a a a m a b a b
Algebra / Trig Final Exa Study Guide (Fall Seester) Moncada/Dunphy Inforation About the Final Exa The final exa is cuulative, covering Appendix A (A.1-A.5) and Chapter 1. All probles will be ultiple choice
More informationAnalysis of Polynomial & Rational Functions ( summary )
Analysis of Polynoial & Rational Functions ( suary ) The standard for of a polynoial function is ( ) where each of the nubers are called the coefficients. The polynoial of is said to have degree n, where
More informationMATHEMATICS 9 CHAPTER 7 MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT NAME: DATE: BLOCK: TEACHER: Miller High School Mathematics Page 1
MATHEMATICS 9 CHAPTER 7 NAME: DATE: BLOCK: TEACHER: MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT Miller High School Mathematics Page 1 Day 1: Creating expressions with algebra tiles 1. Determine the multiplication
More informationChapter 6. Polynomials
Chapter 6 Polynomials How to Play the Stock Market 6.1 Monomials: Multiplication and Division 6.2 Polynomials 6.3 Addition and Subtraction of Polynomials 6.4 Multiplication of Polynomials Chapter Review
More 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 informationSection 10-1: Laws of Exponents
Section -: Laws of Eponents Learning Outcome Multiply: - ( ) = - - = = To multiply like bases, add eponents, and use common base. Rewrite answer with positive eponent. Learning Outcome Write the reciprocals
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 informationPolynomials. Exponents. End Behavior. Writing. Solving Factoring. Graphing. End Behavior. Polynomial Notes. Synthetic Division.
Polynomials Polynomials 1. P 1: Exponents 2. P 2: Factoring Polynomials 3. P 3: End Behavior 4. P 4: Fundamental Theorem of Algebra Writing real root x= 10 or (x+10) local maximum Exponents real root x=10
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 informationDegree 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
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 informationStandard & Canonical Forms
Standard & Canonical Fors CHAPTER OBJECTIVES Learn Binary Logic and BOOLEAN AlgebraLearn How to ap a Boolean Expression into Logic Circuit Ipleentation Learn How To anipulate Boolean Expressions and Siplify
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 informationStudy Guide for Math 095
Study Guide for Math 095 David G. Radcliffe November 7, 1994 1 The Real Number System Writing a fraction in lowest terms. 1. Find the largest number that will divide into both the numerator and the denominator.
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 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 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 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 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 information3.3 Dividing Polynomials. Copyright Cengage Learning. All rights reserved.
3.3 Dividing Polynomials Copyright Cengage Learning. All rights reserved. Objectives Long Division of Polynomials Synthetic Division The Remainder and Factor Theorems 2 Dividing Polynomials In this section
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 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 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 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 informationAlgebra 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
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 informationAlgebra. Practice Pack
Algebra Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Algebra Basics Practice 1 What Are Negative and Positive Numbers?... 1 Practice 2 Larger and Smaller Numbers................ 2 Practice
More informationPolynomials 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 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 informationFactorisation CHAPTER Introduction
FACTORISATION 217 Factorisation CHAPTER 14 14.1 Introduction 14.1.1 Factors of natural numbers You will remember what you learnt about factors in Class VI. Let us take a natural number, say 30, and write
More informationAppendix: Synthetic Division
Appendix: Synthetic Division AP Learning Objectives In this section, we will learn how to: 1. Divide polynomials using synthetic division. Synthetic division is a short form of long division with polynomials.
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 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 informationAlgebra 2 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 nine specific concepts covered in the
More informationPre-Algebra 2. Unit 9. Polynomials Name Period
Pre-Algebra Unit 9 Polynomials Name Period 9.1A Add, Subtract, and Multiplying Polynomials (non-complex) Explain Add the following polynomials: 1) ( ) ( ) ) ( ) ( ) Subtract the following polynomials:
More informationSect Properties of Real Numbers and Simplifying Expressions
Sect 1.7 - Properties of Real Numbers and Simplifying Expressions Concept #1 Commutative Properties of Real Numbers Ex. 1a 9.34 + 2.5 Ex. 1b 2.5 + ( 9.34) Ex. 1c 6.3(4.2) Ex. 1d 4.2( 6.3) a) 9.34 + 2.5
More informationExample #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
More informationALGEBRA 2 Summer Review Assignments Graphing
ALGEBRA 2 Summer Review Assignments Graphing To be prepared for algebra two, and all subsequent math courses, you need to be able to accurately and efficiently find the slope of any line, be able to write
More informationGeometry 21 Summer Work Packet Review and Study Guide
Geometry Summer Work Packet Review and Study Guide This study guide is designed to accompany the Geometry Summer Work Packet. Its purpose is to offer a review of the ten specific concepts covered in the
More informationAlgebraic 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
More informationDue 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.
More informationHow 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
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 informationIES Parque Lineal - 2º ESO
UNIT5. ALGEBRA Contenido 1. Algebraic expressions.... 1 Worksheet: algebraic expressions.... 2 2. Monomials.... 3 Worksheet: monomials.... 5 3. Polynomials... 6 Worksheet: polynomials... 9 4. Factorising....
More informationFactor each expression. Remember, always find the GCF first. Then if applicable use the x-box method and also look for difference of squares.
NOTES 11: RATIONAL EXPRESSIONS AND EQUATIONS Name: Date: Period: Mrs. Nguyen s Initial: LESSON 11.1 SIMPLIFYING RATIONAL EXPRESSIONS Lesson Preview Review Factoring Skills and Simplifying Fractions Factor
More informationA field trips costs $800 for the charter bus plus $10 per student for x students. The cost per student is represented by: 10x x
LEARNING STRATEGIES: Activate Prior Knowledge, Shared Reading, Think/Pair/Share, Note Taking, Group Presentation, Interactive Word Wall A field trips costs $800 for the charter bus plus $10 per student
More informationEvaluate algebraic expressions for given values of the variables.
Algebra I Unit Lesson Title Lesson Objectives 1 FOUNDATIONS OF ALGEBRA Variables and Expressions Exponents and Order of Operations Identify a variable expression and its components: variable, coefficient,
More informationChapter 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
More informationHSED Math Course Outcome Summary
Wisconsin Technical College System HSED 5.09 - Math Course Outcome Summary Course Information Description Learners will apply math concepts in real-world context including financial literacy consumer applications.
More informationDepartamento de Matematicas. Real Instituto de Jovellanos. J. F. Antona Algebraic notation and Polynomials 1
Departamento de Matematicas. Real Instituto de Jovellanos. J. F. Antona Algebraic notation and Polynomials 1 Algebraic Notation The ability to convert worded sentences and problems into algebraic symbols
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 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 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 informationx 9 or x > 10 Name: Class: Date: 1 How many natural numbers are between 1.5 and 4.5 on the number line?
1 How many natural numbers are between 1.5 and 4.5 on the number line? 2 How many composite numbers are between 7 and 13 on the number line? 3 How many prime numbers are between 7 and 20 on the number
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 informationarxiv: v1 [math.nt] 14 Sep 2014
ROTATION REMAINDERS P. JAMESON GRABER, WASHINGTON AND LEE UNIVERSITY 08 arxiv:1409.411v1 [ath.nt] 14 Sep 014 Abstract. We study properties of an array of nubers, called the triangle, in which each row
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 informationPOLYNOMIALS. Maths 4 th ESO José Jaime Noguera
POLYNOMIALS Maths 4 th ESO José Jaime Noguera 1 Algebraic expressions Book, page 26 YOUR TURN: exercises 1, 2, 3. Exercise: Find the numerical value of the algebraic expression xy 2 8x + y, knowing that
More informationDividing Polynomials: Remainder and Factor Theorems
Dividing Polynomials: Remainder and Factor Theorems When we divide one polynomial by another, we obtain a quotient and a remainder. If the remainder is zero, then the divisor is a factor of the dividend.
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 informationPolynomials. Chapter 6. Vocabulary. 6.1 Introduction to polynomials. Term. Polynomial. Coefficient. Degree of a term. Degree of a polynomial
Chapter 6 Polynomials Vocabulary Term Polynomial Coefficient Degree of a term Degree of a polynomial Leading term Descending order Like terms Scientific notation Distributive law 6.1 Introduction to polynomials
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 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
More informationPart 2 - Beginning Algebra Summary
Part - Beginning Algebra Summary Page 1 of 4 1/1/01 1. Numbers... 1.1. Number Lines... 1.. Interval Notation.... Inequalities... 4.1. Linear with 1 Variable... 4. Linear Equations... 5.1. The Cartesian
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 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 informationLinear Equations & Inequalities Definitions
Linear Equations & Inequalities Definitions Constants - a term that is only a number Example: 3; -6; -10.5 Coefficients - the number in front of a term Example: -3x 2, -3 is the coefficient Variable -
More informationMath Refresher #1. Lucy C. Sorensen Assistant Professor of Public Administration & Policy
Math Refresher #1 Lucy C. Sorensen Assistant Professor of Public Administration & Policy Agenda Why Are You Here? What Should You Do Next? Unit 1 Topics: Negative numbers Order of operations Algebraic
More informationPolynomials Practice Test
Name: Class: Date: Polynomials Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. From the list, which terms are like 7x? 7x 2, 6x, 5, 8x, 7x,
More 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 informationReal Numbers. Real numbers are divided into two types, rational numbers and irrational numbers
Real Numbers Real numbers are divided into two types, rational numbers and irrational numbers I. Rational Numbers: Any number that can be expressed as the quotient of two integers. (fraction). Any number
More 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 informationChapter. Algebra techniques. Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations.
Chapter 2 Algebra techniques Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations. Page 1 2.1 What is algebra? In order to extend the usefulness of mathematical
More informationAlgebra I. abscissa the distance along the horizontal axis in a coordinate graph; graphs the domain.
Algebra I abscissa the distance along the horizontal axis in a coordinate graph; graphs the domain. absolute value the numerical [value] when direction or sign is not considered. (two words) additive inverse
More informationCoach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers
Coach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers CLASSIFICATIONS OF NUMBERS NATURAL NUMBERS = N = {1,2,3,4,...}
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 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 informationMath 0320 Final Exam Review
Math 0320 Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Factor out the GCF using the Distributive Property. 1) 6x 3 + 9x 1) Objective:
More informationSOLVING LITERAL EQUATIONS. Bundle 1: Safety & Process Skills
SOLVING LITERAL EQUATIONS Bundle 1: Safety & Process Skills Solving Literal Equations An equation is a atheatical sentence with an equal sign. The solution of an equation is a value for a variable that
More informationMath 1600A Lecture 3, Section 002
Math 1600 Lecture 3 1 of 5 Math 1600A Lecture 3, Section 002 Announceents: More texts, solutions anuals and packages coing soon. Read Section 1.3 for next class. Work through recoended hoework questions.
More information4.3 Division of Polynomials
4.3 Division of Polynomials Learning Objectives Divide a polynomials by a monomial. Divide a polynomial by a binomial. Rewrite and graph rational functions. Introduction A rational epression is formed
More informationAlgebra One Dictionary
Algebra One Dictionary Page 1 of 17 A Absolute Value - the distance between the number and 0 on a number line Algebraic Expression - An expression that contains numbers, operations and at least one variable.
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 informationCommon Core Standards Addressed in this Resource
Common Core Standards Addressed in this Resource 6.RP.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,
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 informationPolygonal Designs: Existence and Construction
Polygonal Designs: Existence and Construction John Hegean Departent of Matheatics, Stanford University, Stanford, CA 9405 Jeff Langford Departent of Matheatics, Drake University, Des Moines, IA 5011 G
More informationP.5 Solving Equations
PRC Ch P_5.notebook P.5 Solving Equations What you should learn How to solve linear equations How to solve quadratic equations equations How to solve polynomial equations of degree three or higher How
More informationTABLE OF CONTENTS INTRODUCTION. Supplementary Requirements Credit Hours Administrative Instructions Grading and Certification Instruction
TABLE OF CONTENTS INTRODUCTION Supplementary Requirements Credit Hours Administrative Instructions Grading and Certification Instruction LESSON 1: ALGEBRA (Tasks. This lesson is common to all missile repairer
More informationBeginning 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:
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 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 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 informationMA094 Part 2 - Beginning Algebra Summary
MA094 Part - Beginning Algebra Summary Page of 8/8/0 Big Picture Algebra is Solving Equations with Variables* Variable Variables Linear Equations x 0 MA090 Solution: Point 0 Linear Inequalities x < 0 page
More informationUNIT 3: POLYNOMIALS AND ALGEBRAIC FRACTIONS. A polynomial is an algebraic expression that consists of a sum of several monomials. x n 1...
UNIT 3: POLYNOMIALS AND ALGEBRAIC FRACTIONS. Polynomials: A polynomial is an algebraic expression that consists of a sum of several monomials. Remember that a monomial is an algebraic expression as ax
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 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 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 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 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 information