Math 25 Activity 6: Factoring Advanced
|
|
- Marian Walsh
- 5 years ago
- Views:
Transcription
1 Instructor! Math 25 Activity 6: Factoring Advanced Last week we looked at greatest common factors and the basics of factoring out the GCF. In this second activity, we will discuss factoring more difficult polynomials. We begin by reviewing a more complex GCF. 1. Find the greatest common factor of and, then factor. Your instructor will give you time to do this in a group and then explain on the whiteboard. Remember that when you factor, you find the GCF of all the terms, then divide each term by the GCF, then re-write the expression in parentheses putting the GCF in front which indicates multiplication. 2. Find the greatest common factor of and, then factor. Your instructor will give you time to do this in a group and then explain on the whiteboard. In this problem, the GCF is actually a binomial itself. We continue with what is called factoring by grouping. Recall in a previous activity, we can group terms that are being added using the associative property of addition. When we have four terms, but none of them have a common factor, then we can try grouping them into pairs to see if that leads us to factoring the whole polynomial. Consider the following example explained step by step. Notice that the four terms do not have a common factor other than one. Look for a way to pair two terms together that have a common factor, then pair the last two terms together. The greatest common factor in the first grouping is 2, so factor the 2 from just the first two terms. The greatest common factor in the second grouping is u, so factor the u from just the second two terms. Notice how there are only two terms now and they are separated by a plus sign. Factor your new algebraic expression as you did in problem 2. Note: By the commutative property of multiplication, is the same as Page 1 of 5
2 Instructor! 3. Now as a group, try a similar example and write a short note explaining what you did in that step. We have given you the answer to let you check your work. Your instructor will give you time to do this in a group and then explain on the whiteboard. Try another example of factoring by grouping, except this time there are negative signs involved. Be careful when you factor out a negative number! 4. Try a similar example and write a short note explaining what you did in that step. We have given you the answer to let you check your work. 5. Factor yx 2y 4x + 8 Your instructor can explain the steps for these two problems on a whiteboard before continuing to the next skill. Page 2 of 5
3 Now that you have seen the skill that is called factor by grouping we can move to the last factoring skill we will go over in these activities. Note: There are MANY ways to factor trinomials. If you know how to factor trinomials quickly and accurately, then just practice factoring these examples your way. If you do not know how to factor, or you want to see another method, then practice these using this method. The goal is to factor a trinomial, which means we have three terms. We will do an example with each step explained, then you will spend the rest of the activity practicing these steps. You may need scratch paper for some of the in-between steps. PROBLEM s STEPS STEP NOTES SCRATCH PAPER WORK Notice that the three terms do not have a common factor other than one. Label the coefficients so that the number before is the a coefficient, the number before is the b coefficient, and the number at the end is the c coefficient. Multiply List all the pairs that multiply to (from the previous step). Make sure to list them in order and stop listing before repeating yourself. Find the pair which adds to b. Since, we want to pick because = 11 Rewrite the middle term as the sum you found in the previous step. 3+8 = 11 so instead of write Make sure you have four terms now and pair them like you did in the factor by grouping problems. Find the GCF of each pair and factor each pair like you did in factor by grouping. Look for the GCF (which should be in the parentheses these should always match at this point) like you did with factor by grouping. Distribute to check your answer. Page 3 of 5
4 This example of what is called the AC Method of Factoring can work on most trinomials. It gets faster the more you practice it and it removes the guessing from factoring. 6. Try factoring the expression using the AC Method. Make sure you understand all the steps you wrote. Writing notes to yourself will help you follow your notes later. The answer should be. Students also need to think about negative signs. How can you tell when you need to add negative signs to a problem? Here are the four types of signs you can end up with, and what to do about the negative signs (this is why we list the pairs in order, without repeating): SITUATION EXAMPLE WHAT TO DO WHAT THE LIST LOOKS LIKE is positive multiply to, then all the positive is positive multiply to, then all the negative numbers are negative. is negative multiply to, then only the positive list of smaller numbers are negative and the list of larger is negative negative multiply to, then only the list of larger numbers are negative and the list of smaller Page 4 of 5
5 When it comes to factoring, practice and repetition really make a big difference. Students who practice factoring about 10 different trinomials each day will feel more comfortable with factoring, especially later in future math classes where factoring is an assumed skill necessary to finish more difficult problems. We do not have time to go over all the examples of factoring, but will leave lists of expressions that you can put on flashcards to practice factoring. Here is a formula for the special case of factoring a difference of squares: Some of these are more difficult than others. Trinomials: Binomials: Page 5 of 5
Chapter R.4 Factoring Polynomials
Chapter R.4 Factoring Polynomials Introduction to Factoring To factor an expression means to write the expression as a product of two or more factors. Sample Problem: Factor each expression. a. 15 b. x
Greatest Common Factor (GCF) Factoring
Section 4 4: Greatest Common Factor (GCF) Factoring The last chapter introduced the distributive process. The distributive process takes a product of a monomial and a polynomial and changes the multiplication
Factoring and Applications
Factoring and Applications What is a factor? The Greatest Common Factor (GCF) To factor a number means to write it as a product (multiplication). Therefore, in the problem 48 3, 4 and 8 are called the
5 means to write it as a product something times something instead of a sum something plus something plus something.
Intermediate algebra Class notes Factoring Introduction (section 6.1) Recall we factor 10 as 5. Factoring something means to think of it as a product! Factors versus terms: terms: things we are adding
In algebra, factor by rewriting a polynomial as a product of lower-degree polynomials
Algebra 2 Notes SOL AII.1 Factoring Polynomials Mrs. Grieser Name: Date: Block: Factoring Review Factor: rewrite a number or expression as a product of primes; e.g. 6 = 2 3 In algebra, factor by rewriting
1.3 Polynomials and Factoring
1.3 Polynomials and Factoring Polynomials Constant: a number, such as 5 or 27 Variable: a letter or symbol that represents a value. Term: a constant, variable, or the product or a constant and variable.
How To Factor By Gcf In Algebra 1.5
7-2 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Simplify. 1. 2(w + 1) 2. 3x(x 2 4) 2w + 2 3x 3 12x Find the GCF of each pair of monomials. 3. 4h 2 and 6h 2h 4. 13p and 26p
Factoring Quadratic Expressions
Factoring the trinomial ax 2 + bx + c when a = 1 A trinomial in the form x 2 + bx + c can be factored to equal (x + m)(x + n) when the product of m x n equals c and the sum of m + n equals b. (Note: the
Name Intro to Algebra 2. Unit 1: Polynomials and Factoring
Name Intro to Algebra 2 Unit 1: Polynomials and Factoring Date Page Topic Homework 9/3 2 Polynomial Vocabulary No Homework 9/4 x In Class assignment None 9/5 3 Adding and Subtracting Polynomials Pg. 332
NSM100 Introduction to Algebra Chapter 5 Notes Factoring
Section 5.1 Greatest Common Factor (GCF) and Factoring by Grouping Greatest Common Factor for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial. GCF is the
Factoring Polynomials
Factoring Polynomials Factoring Factoring is the process of writing a polynomial as the product of two or more polynomials. The factors of 6x 2 x 2 are 2x + 1 and 3x 2. In this section, we will be factoring
Factoring (pp. 1 of 4)
Factoring (pp. 1 of 4) Algebra Review Try these items from middle school math. A) What numbers are the factors of 4? B) Write down the prime factorization of 7. C) 6 Simplify 48 using the greatest common
Tool 1. Greatest Common Factor (GCF)
Chapter 4: Factoring Review Tool 1 Greatest Common Factor (GCF) This is a very important tool. You must try to factor out the GCF first in every problem. Some problems do not have a GCF but many do. When
Factoring Trinomials of the Form x 2 bx c
4.2 Factoring Trinomials of the Form x 2 bx c 4.2 OBJECTIVES 1. Factor a trinomial of the form x 2 bx c 2. Factor a trinomial containing a common factor NOTE The process used to factor here is frequently
Factoring Algebra- Chapter 8B Assignment Sheet
Name: Factoring Algebra- Chapter 8B Assignment Sheet Date Section Learning Targets Assignment Tues 2/17 Find the prime factorization of an integer Find the greatest common factor (GCF) for a set of monomials.
Section 6.1 Factoring Expressions
Section 6.1 Factoring Expressions The first method we will discuss, in solving polynomial equations, is the method of FACTORING. Before we jump into this process, you need to have some concept of what
FACTORING TRINOMIALS IN THE FORM OF ax 2 + bx + c
Tallahassee Community College 55 FACTORING TRINOMIALS IN THE FORM OF ax 2 + bx + c This kind of trinomial differs from the previous kind we have factored because the coefficient of x is no longer "1".
expression is written horizontally. The Last terms ((2)( 4)) because they are the last terms of the two polynomials. This is called the FOIL method.
A polynomial of degree n (in one variable, with real coefficients) is an expression of the form: a n x n + a n 1 x n 1 + a n 2 x n 2 + + a 2 x 2 + a 1 x + a 0 where a n, a n 1, a n 2, a 2, a 1, a 0 are
AIP Factoring Practice/Help
The following pages include many problems to practice factoring skills. There are also several activities with examples to help you with factoring if you feel like you are not proficient with it. There
EAP/GWL Rev. 1/2011 Page 1 of 5. Factoring a polynomial is the process of writing it as the product of two or more polynomial factors.
EAP/GWL Rev. 1/2011 Page 1 of 5 Factoring a polynomial is the process of writing it as the product of two or more polynomial factors. Example: Set the factors of a polynomial equation (as opposed to an
When factoring, we look for greatest common factor of each term and reverse the distributive property and take out the GCF.
Factoring: reversing the distributive property. The distributive property allows us to do the following: When factoring, we look for greatest common factor of each term and reverse the distributive property
Definitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder).
Math 50, Chapter 8 (Page 1 of 20) 8.1 Common Factors Definitions 1. A factor of integer is an integer that will divide the given integer evenly (with no remainder). Find all the factors of a. 44 b. 32
Academic Success Centre
250) 960-6367 Factoring Polynomials Sometimes when we try to solve or simplify an equation or expression involving polynomials the way that it looks can hinder our progress in finding a solution. Factorization
( ) FACTORING. x In this polynomial the only variable in common to all is x.
FACTORING Factoring is similar to breaking up a number into its multiples. For example, 10=5*. The multiples are 5 and. In a polynomial it is the same way, however, the procedure is somewhat more complicated
The Greatest Common Factor; Factoring by Grouping
296 CHAPTER 5 Factoring and Applications 5.1 The Greatest Common Factor; Factoring by Grouping OBJECTIVES 1 Find the greatest common factor of a list of terms. 2 Factor out the greatest common factor.
Factoring Guidelines. Greatest Common Factor Two Terms Three Terms Four Terms. 2008 Shirley Radai
Factoring Guidelines Greatest Common Factor Two Terms Three Terms Four Terms 008 Shirley Radai Greatest Common Factor 008 Shirley Radai Factoring by Finding the Greatest Common Factor Always check for
A Systematic Approach to Factoring
A Systematic Approach to Factoring Step 1 Count the number of terms. (Remember****Knowing the number of terms will allow you to eliminate unnecessary tools.) Step 2 Is there a greatest common factor? Tool
FACTORING ax 2 bx c WITH a 1
296 (6 20) Chapter 6 Factoring 6.4 FACTORING a 2 b c WITH a 1 In this section The ac Method Trial and Error Factoring Completely In Section 6.3 we factored trinomials with a leading coefficient of 1. In
Factoring. Factoring Monomials Monomials can often be factored in more than one way.
Factoring Factoring is the reverse of multiplying. When we multiplied monomials or polynomials together, we got a new monomial or a string of monomials that were added (or subtracted) together. For example,
Factoring Flow Chart
Factoring Flow Chart greatest common factor? YES NO factor out GCF leaving GCF(quotient) how many terms? 4+ factor by grouping 2 3 difference of squares? perfect square trinomial? YES YES NO NO a 2 -b
Factoring Polynomials and Solving Quadratic Equations
Factoring Polynomials and Solving Quadratic Equations Math Tutorial Lab Special Topic Factoring Factoring Binomials Remember that a binomial is just a polynomial with two terms. Some examples include 2x+3
4.4 Factoring ax 2 + bx + c
4.4 Factoring ax 2 + bx + c From the last section, we now know a trinomial should factor as two binomials. With this in mind, we need to look at how to factor a trinomial when the leading coefficient is
This is Factoring and Solving by Factoring, chapter 6 from the book Beginning Algebra (index.html) (v. 1.0).
This is Factoring and Solving by Factoring, chapter 6 from the book Beginning Algebra (index.html) (v. 1.0). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/
MATH 90 CHAPTER 6 Name:.
MATH 90 CHAPTER 6 Name:. 6.1 GCF and Factoring by Groups Need To Know Definitions How to factor by GCF How to factor by groups The Greatest Common Factor Factoring means to write a number as product. a
6.1 The Greatest Common Factor; Factoring by Grouping
386 CHAPTER 6 Factoring and Applications 6.1 The Greatest Common Factor; Factoring by Grouping OBJECTIVES 1 Find the greatest common factor of a list of terms. 2 Factor out the greatest common factor.
Factoring Methods. Example 1: 2x + 2 2 * x + 2 * 1 2(x + 1)
Factoring Methods When you are trying to factor a polynomial, there are three general steps you want to follow: 1. See if there is a Greatest Common Factor 2. See if you can Factor by Grouping 3. See if
Factoring Trinomials: The ac Method
6.7 Factoring Trinomials: The ac Method 6.7 OBJECTIVES 1. Use the ac test to determine whether a trinomial is factorable over the integers 2. Use the results of the ac test to factor a trinomial 3. For
Using the ac Method to Factor
4.6 Using the ac Method to Factor 4.6 OBJECTIVES 1. Use the ac test to determine factorability 2. Use the results of the ac test 3. Completely factor a trinomial In Sections 4.2 and 4.3 we used the trial-and-error
CHAPTER 7: FACTORING POLYNOMIALS
CHAPTER 7: FACTORING POLYNOMIALS FACTOR (noun) An of two or more quantities which form a product when multiplied together. 1 can be rewritten as 3*, where 3 and are FACTORS of 1. FACTOR (verb) - To factor
SIMPLIFYING ALGEBRAIC FRACTIONS
Tallahassee Community College 5 SIMPLIFYING ALGEBRAIC FRACTIONS In arithmetic, you learned that a fraction is in simplest form if the Greatest Common Factor (GCF) of the numerator and the denominator is
Operations with Algebraic Expressions: Multiplication of Polynomials
Operations with Algebraic Expressions: Multiplication of Polynomials The product of a monomial x monomial To multiply a monomial times a monomial, multiply the coefficients and add the on powers with the
A. Factoring out the Greatest Common Factor.
DETAILED SOLUTIONS AND CONCEPTS - FACTORING POLYNOMIAL EXPRESSIONS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you!
FACTORING ax 2 bx c. Factoring Trinomials with Leading Coefficient 1
5.7 Factoring ax 2 bx c (5-49) 305 5.7 FACTORING ax 2 bx c In this section In Section 5.5 you learned to factor certain special polynomials. In this section you will learn to factor general quadratic polynomials.
2x 2x 2 8x. Now, let s work backwards to FACTOR. We begin by placing the terms of the polynomial inside the cells of the box. 2x 2
Activity 23 Math 40 Factoring using the BOX Team Name (optional): Your Name: Partner(s): 1. (2.) Task 1: Factoring out the greatest common factor Mini Lecture: Factoring polynomials is our focus now. Factoring
The majority of college students hold credit cards. According to the Nellie May
CHAPTER 6 Factoring Polynomials 6.1 The Greatest Common Factor and Factoring by Grouping 6. Factoring Trinomials of the Form b c 6.3 Factoring Trinomials of the Form a b c and Perfect Square Trinomials
Factoring Special Polynomials
6.6 Factoring Special Polynomials 6.6 OBJECTIVES 1. Factor the difference of two squares 2. Factor the sum or difference of two cubes In this section, we will look at several special polynomials. These
6.4 Special Factoring Rules
6.4 Special Factoring Rules OBJECTIVES 1 Factor a difference of squares. 2 Factor a perfect square trinomial. 3 Factor a difference of cubes. 4 Factor a sum of cubes. By reversing the rules for multiplication
Factoring Trinomials of the Form
Section 4 6B: Factoring Trinomials of the Form A x 2 + Bx + C where A > 1 by The AC and Factor By Grouping Method Easy Trinomials: 1 x 2 + Bx + C The last section covered the topic of factoring second
Algebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.
Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear
SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS
(Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic
Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III
Alum Rock Elementary Union School District Algebra I Study Guide for Benchmark III Name Date Adding and Subtracting Polynomials Algebra Standard 10.0 A polynomial is a sum of one ore more monomials. Polynomial
Algebra 1 Chapter 08 review
Name: Class: Date: ID: A Algebra 1 Chapter 08 review Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify the difference. 1. (4w 2 4w 8) (2w 2 + 3w 6)
Factors and Products
CHAPTER 3 Factors and Products What You ll Learn use different strategies to find factors and multiples of whole numbers identify prime factors and write the prime factorization of a number find square
6.3 FACTORING ax 2 bx c WITH a 1
290 (6 14) Chapter 6 Factoring e) What is the approximate maximum revenue? f) Use the accompanying graph to estimate the price at which the revenue is zero. y Revenue (thousands of dollars) 300 200 100
Factoring Polynomials
Factoring a Polynomial Expression Factoring a polynomial is expressing the polynomial as a product of two or more factors. Simply stated, it is somewhat the reverse process of multiplying. To factor polynomials,
Factoring a Difference of Two Squares. Factoring a Difference of Two Squares
284 (6 8) Chapter 6 Factoring 87. Tomato soup. The amount of metal S (in square inches) that it takes to make a can for tomato soup is a function of the radius r and height h: S 2 r 2 2 rh a) Rewrite this
7-6. Choosing a Factoring Model. Extension: Factoring Polynomials with More Than One Variable IN T RO DUC E T EACH. Standards for Mathematical Content
7-6 Choosing a Factoring Model Extension: Factoring Polynomials with More Than One Variable Essential question: How can you factor polynomials with more than one variable? What is the connection between
In the above, the number 19 is an example of a number because its only positive factors are one and itself.
Math 100 Greatest Common Factor and Factoring by Grouping (Review) Factoring Definition: A factor is a number, variable, monomial, or polynomial which is multiplied by another number, variable, monomial,
Factoring A Quadratic Polynomial
Factoring A Quadratic Polynomial If we multiply two binomials together, the result is a quadratic polynomial: This multiplication is pretty straightforward, using the distributive property of multiplication
POLYNOMIALS and FACTORING
POLYNOMIALS and FACTORING Exponents ( days); 1. Evaluate exponential expressions. Use the product rule for exponents, 1. How do you remember the rules for exponents?. How do you decide which rule to use
FACTORING OUT COMMON FACTORS
278 (6 2) Chapter 6 Factoring 6.1 FACTORING OUT COMMON FACTORS In this section Prime Factorization of Integers Greatest Common Factor Finding the Greatest Common Factor for Monomials Factoring Out the
Algebra 2 PreAP. Name Period
Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for completing
Name Date Class Period. How can you use the box method to factor a quadratic trinomial?
Name Date Class Period Activity 9.6 Factoring Using the Box Method MATERIALS QUESTION EXPLORE 1 activity worksheet How can you use the box method to factor a quadratic trinomial? Factor 3x 2 + 16x + 5
5.1 FACTORING OUT COMMON FACTORS
C H A P T E R 5 Factoring he sport of skydiving was born in the 1930s soon after the military began using parachutes as a means of deploying troops. T Today, skydiving is a popular sport around the world.
15.1 Factoring Polynomials
LESSON 15.1 Factoring Polynomials Use the structure of an expression to identify ways to rewrite it. Also A.SSE.3? ESSENTIAL QUESTION How can you use the greatest common factor to factor polynomials? EXPLORE
Unit 12: Introduction to Factoring. Learning Objectives 12.2
Unit 1 Table of Contents Unit 1: Introduction to Factoring Learning Objectives 1. Instructor Notes The Mathematics of Factoring Teaching Tips: Challenges and Approaches Additional Resources Instructor
Adding and Subtracting Fractions. 1. The denominator of a fraction names the fraction. It tells you how many equal parts something is divided into.
Tallahassee Community College Adding and Subtracting Fractions Important Ideas:. The denominator of a fraction names the fraction. It tells you how many equal parts something is divided into.. The numerator
Introduction Assignment
PRE-CALCULUS 11 Introduction Assignment Welcome to PREC 11! This assignment will help you review some topics from a previous math course and introduce you to some of the topics that you ll be studying
a. You can t do the simple trick of finding two integers that multiply to give 6 and add to give 5 because the a (a = 4) is not equal to one.
FACTORING TRINOMIALS USING THE AC METHOD. Factoring trinomial epressions in one unknown is an important skill necessary to eventually solve quadratic equations. Trinomial epressions are of the form a 2
HIBBING COMMUNITY COLLEGE COURSE OUTLINE
HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE: - Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,
Veterans Upward Bound Algebra I Concepts - Honors
Veterans Upward Bound Algebra I Concepts - Honors Brenda Meery Kaitlyn Spong Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) www.ck12.org Chapter 6. Factoring CHAPTER
By reversing the rules for multiplication of binomials from Section 4.6, we get rules for factoring polynomials in certain forms.
SECTION 5.4 Special Factoring Techniques 317 5.4 Special Factoring Techniques OBJECTIVES 1 Factor a difference of squares. 2 Factor a perfect square trinomial. 3 Factor a difference of cubes. 4 Factor
x 4-1 = (x²)² - (1)² = (x² + 1) (x² - 1) = (x² + 1) (x - 1) (x + 1)
Factoring Polynomials EXAMPLES STEP 1 : Greatest Common Factor GCF Factor out the greatest common factor. 6x³ + 12x²y = 6x² (x + 2y) 5x - 5 = 5 (x - 1) 7x² + 2y² = 1 (7x² + 2y²) 2x (x - 3) - (x - 3) =
SOLVING QUADRATIC EQUATIONS BY THE NEW TRANSFORMING METHOD (By Nghi H Nguyen Updated Oct 28, 2014))
SOLVING QUADRATIC EQUATIONS BY THE NEW TRANSFORMING METHOD (By Nghi H Nguyen Updated Oct 28, 2014)) There are so far 8 most common methods to solve quadratic equations in standard form ax² + bx + c = 0.
6.6 Factoring Strategy
456 CHAPTER 6. FACTORING 6.6 Factoring Strategy When you are concentrating on factoring problems of a single type, after doing a few you tend to get into a rhythm, and the remainder of the exercises, because
Polynomials and Factoring
7.6 Polynomials and Factoring Basic Terminology A term, or monomial, is defined to be a number, a variable, or a product of numbers and variables. A polynomial is a term or a finite sum or difference of
Pre-Calculus II Factoring and Operations on Polynomials
Factoring... 1 Polynomials...1 Addition of Polynomials... 1 Subtraction of Polynomials...1 Multiplication of Polynomials... Multiplying a monomial by a monomial... Multiplying a monomial by a polynomial...
Big Bend Community College. Beginning Algebra MPC 095. Lab Notebook
Big Bend Community College Beginning Algebra MPC 095 Lab Notebook Beginning Algebra Lab Notebook by Tyler Wallace is licensed under a Creative Commons Attribution 3.0 Unported License. Permissions beyond
Five 5. Rational Expressions and Equations C H A P T E R
Five C H A P T E R Rational Epressions and Equations. Rational Epressions and Functions. Multiplication and Division of Rational Epressions. Addition and Subtraction of Rational Epressions.4 Comple Fractions.
SPECIAL PRODUCTS AND FACTORS
CHAPTER 442 11 CHAPTER TABLE OF CONTENTS 11-1 Factors and Factoring 11-2 Common Monomial Factors 11-3 The Square of a Monomial 11-4 Multiplying the Sum and the Difference of Two Terms 11-5 Factoring the
SOLVING QUADRATIC EQUATIONS - COMPARE THE FACTORING AC METHOD AND THE NEW TRANSFORMING METHOD (By Nghi H. Nguyen - Jan 18, 2015)
SOLVING QUADRATIC EQUATIONS - COMPARE THE FACTORING AC METHOD AND THE NEW TRANSFORMING METHOD (By Nghi H. Nguyen - Jan 18, 2015) GENERALITIES. When a given quadratic equation can be factored, there are
Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
FACTORING POLYNOMIALS
296 (5-40) Chapter 5 Exponents and Polynomials where a 2 is the area of the square base, b 2 is the area of the square top, and H is the distance from the base to the top. Find the volume of a truncated
Factoring Trinomials using Algebra Tiles Student Activity
Factoring Trinomials using Algebra Tiles Student Activity Materials: Algebra Tiles (student set) Worksheet: Factoring Trinomials using Algebra Tiles Algebra Tiles: Each algebra tile kits should contain
A.3. Polynomials and Factoring. Polynomials. What you should learn. Definition of a Polynomial in x. Why you should learn it
Appendi A.3 Polynomials and Factoring A23 A.3 Polynomials and Factoring What you should learn Write polynomials in standard form. Add,subtract,and multiply polynomials. Use special products to multiply
Title: Factoring Trinomials Using the Trial-and-Error Method Class: Math 100 Author: Sharareh Masooman Instructions to tutor: Read instructions under
Title: Factoring Trinomials Using the Trial-and-Error Method Class: Math 100 Author: Sharareh Masooman nstructions to tutor: Read instructions under Activity and follow all steps for each problem exactly
MATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
Determinants can be used to solve a linear system of equations using Cramer s Rule.
2.6.2 Cramer s Rule Determinants can be used to solve a linear system of equations using Cramer s Rule. Cramer s Rule for Two Equations in Two Variables Given the system This system has the unique solution
Mathematics Placement
Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.
Wentzville School District Algebra 1: Unit 8 Stage 1 Desired Results
Wentzville School District Algebra 1: Unit 8 Stage 1 Desired Results Unit Title: Quadratic Expressions & Equations Course: Algebra I Unit 8 - Quadratic Expressions & Equations Brief Summary of Unit: At
0.8 Rational Expressions and Equations
96 Prerequisites 0.8 Rational Expressions and Equations We now turn our attention to rational expressions - that is, algebraic fractions - and equations which contain them. The reader is encouraged to
Prime Time: Homework Examples from ACE
Prime Time: Homework Examples from ACE Investigation 1: Building on Factors and Multiples, ACE #8, 28 Investigation 2: Common Multiples and Common Factors, ACE #11, 16, 17, 28 Investigation 3: Factorizations:
Simplification Problems to Prepare for Calculus
Simplification Problems to Prepare for Calculus In calculus, you will encounter some long epressions that will require strong factoring skills. This section is designed to help you develop those skills.
6.5 Factoring Special Forms
440 CHAPTER 6. FACTORING 6.5 Factoring Special Forms In this section we revisit two special product forms that we learned in Chapter 5, the first of which was squaring a binomial. Squaring a binomial.
Answers to Basic Algebra Review
Answers to Basic Algebra Review 1. -1.1 Follow the sign rules when adding and subtracting: If the numbers have the same sign, add them together and keep the sign. If the numbers have different signs, subtract
1.3 Algebraic Expressions
1.3 Algebraic Expressions A polynomial is an expression of the form: a n x n + a n 1 x n 1 +... + a 2 x 2 + a 1 x + a 0 The numbers a 1, a 2,..., a n are called coefficients. Each of the separate parts,
Factoring ax 2 + bx + c - Teacher Notes
Southern Nevada Regional Professi onal D evel opment Program VOLUME 1, ISSUE 8 MAY 009 A N ewsletter from the Sec ondary Mathematic s Team Factoring ax + bx + c - Teacher Notes Here we look at sample teacher