# Topic: Special Products and Factors Subtopic: Rules on finding factors of polynomials

Save this PDF as:
Size: px
Start display at page:

Download "Topic: Special Products and Factors Subtopic: Rules on finding factors of polynomials" ## Transcription

1 Quarter I: Special Products and Factors and Quadratic Equations Topic: Special Products and Factors Subtopic: Rules on finding factors of polynomials Time Frame: 20 days Time Frame: 3 days Content Standard: The learner demonstrates understanding of the key concepts on the rules applied to finding factors. Stage 1 Performance Standard: The learner formulates real-life problems involving factors and analyze these using a variety of strategies with utmost accuracy. Essential Understanding(s): Patterns in finding factors of polynomials to facilitate the analysis of real- life situations. Essential Question(s): Why do we need to study the rules in factoring? How are patterns used to analyze real-life problems involving factoring of polynomials? The learner will know: rules on finding common monomial factors. factoring trinomials. factoring perfect square trinomials factoring difference of two squares factoring sum or difference of two cubes factoring by grouping apply the concept on rules on factoring in the analysis of real- life situation Product or Performance Task: Problems formulated are real life. involve factors of algebraic expressions. are analyzed through The learner will be able to: explore the rules in finding common factors and search for patterns. factor trinomials. factor perfect square trinomials factor difference of two squares factor sum or difference of two cubes factor by grouping apply the concept on rules on factoring in the analysis of real- life situations. Stage 2 Evidence at the level of understanding The learner should be able to demonstrate understanding of factoring using the six (6) facets of understanding: Explanation Discuss how factors are found using different methods. Evidence at the level of performance Performance assessment of problems formulated based on the following suggested criteria: real-life situations

2 appropriate and accurate representations Clear Coherent Thorough Interpretation State the process of finding special products of two integers and relate it to the patterns in getting the product of two binomials. Creative Illustrative Meaningful Application Pose situations in real life involving special products and analyze them. Appropriate Authentic Practical Perspective Compare and contrast the different ways of finding special products. Credible Critical Realistic Empathy Describe the difficulties one can experience without knowing the process of getting special products. Open Responsive & Sensitive situations involve factors situations are analyzed through appropriate representations Tools: Rubrics for assessment of problems formulated and analyzed.

3 Self- Knowledge Assess how one can give the best representation to a situation involving special products. Receptive Reflective Relevant Stage 3 Teaching - Learning Sequence: The learners are expected to master the following concepts: 1. Factoring polynomials whose terms have a common monomial factor 2. Factoring trinomials which are product of two binomials. 3. Factoring perfect square trinomials and difference of two squares 4. Applications of the concept of factoring polynomials in the analysis of real-life situations ( Note: Present this activity using manila paper, activity cards, overhead projector, power point presentation, etc.) Introduction Consider the figures at the right. What do you think are the measures of the sides of the rectangle? of the square? ac ad bc bd a 2 ab ab b 2

4 Try this opening activity: A. Consider the rectangular paper on the right side. The area of each part is given. 1. Give the possible lengths of the sides for each part. Explain. 2. Express each area as a factor of the possible sides. 3. If the area of the big rectangle is 616 cm 2, what are the possible measures of the sides? 4. What pattern did you discover? B. Consider each of the following: What are the possible sides if the new areas are as follows: A 36 cm 2 C 96 cm 2 B D 160 cm cm 2 E F 48 cm cm 2 A 36 x 2 cm 2 D 160 x 4 y 6 cm 2 B 132 x 2 y 2 cm 2 E 48 x 8 y 4 cm 2 C 96 x 2 y 4 cm 2 F 144x 2 y 2 cm 2 1. Explore ( Group Work ) Note: You may assign two groups work on the same material. At this stage, the learners are expected to: 1. explore factors that form product of two binomials. 2. identify the factors of two binomials. 3. master the process of finding factors of trinomials.

5 Let us have another piece of rectangular paper similar to the opening activity. This time, let us apply manipulatives to discover the factors of two binomials. Follow strictly the directions written in your activity sheet. Activity 1: ( Groups I &II ) : A. 1. Cut papers similar to the figures on the right. 2. Get the total area of the 6 pieces. 3. Fit the pieces in such a way that they form just one big rectangle ( with no holes and no pieces overlapping). 4. Does the total area change? Why? Why not? x 2 x x x 5. Now, write the measures of the sides of the big rectangle formed. 6. Compare the area of the big rectangle with that of the combined areas of the 6 pieces. 7. Generalize your observation. 1 1 a) x 2 -x -x -x b) x 2 x 2 x 2 x x x 1 1 B. 1. Using the algebra tiles above repeat the process in ( A ).

6 2. Relate the process of finding the factors of an integer to the patterns in getting the factors of a trinomial. Activity 2: ( Group III &IV ) : Figures I and II are two congruent squares. One side of the square in Figure I is ( x+2) units, while the area of the square in Figure II is (x+2)(x+2) sq units. (x + 2) ( x+2)(x+2) A. 1. What is the area of the square with side (x + 2) in factored form? Figure I Figure I 2. What is the side of the square in Figure II if its area is (x +2)(x + 2)? 3. What can you say about (x+2) 2 and (x+2)(x+2)? 4. Now, let us do some manipulative activities. Consider again the tiles used in the previous activity. Form the rectangles using the algebra tiles for the following trinomials. a. x 2 + 4x + 4 b. x 2 + 2x + 1 c. x 2 6x + 9 d. x 2 + 2xy + y 2 4. What do you notice about the four rectangles? Describe and compare their sides. 5. Make a generalization of what you observed. B. 1. Using the procedure learned in (A), determine if the following trinomials follow the same pattern. a. x 2 + 8x + 16 b. x 2 + 5x + 10 c. x 2 4x + 4 d. x 2 10x Relate the process of finding factors of numbers which are perfect squares to the pattern in getting the factors of perfect square trinomials. Activity 3: ( Group V & VI) : 10 cm 1. Using a cartolina, cut a square of side 10 cm 2. Cut off a small square of size 2 cm by 2 cm from one of the corners of the big square paper. 3. Label the side of the big square with 10 cm and (10 2) cm. 2cm

7 4. Cut the remaining paper as shown 5. Rearrange the remaining parts to form a new rectangle. 6. Find the area of a) the original square b) the small square c) new rectangle 7. After cutting out the small square, what is the area of the remaining part of the big square? 8. Make a generalization of what you have discovered. B. 1. Repeat the process in ( A ) using x meters and y meters as the lengths, instead of 10 cm and 2 cm, respectively. 2. Relate the process of finding factors of the difference of two squares using integers and the factors of the difference of two squares using variables. 2. Firm Up A. Answer the following questions: 1. Consider Activity I. a. Using the sides of each part of the square, how will you represent the side of the whole square paper? Explain. b. Write the procedure in getting the common monomial factor of ( 4x +2y ), c. Using the steps in (b), factor the following: i 3x + 9 iv. 6a + 9a + 12ab ii. 8cd - 18 cd 2 v. 3mn + 5 mn 2 iii. 7x 2-21x 3 2. Consider Activity 1 under the Explore. a. How are the sides of a rectangle expressed using the algebra tiles? b. Write the procedure in getting the factors of trinomials which are product of two binomials. x 2 + 3x + 2, x 2-3x + 8 and 3x 2 + 3x + 2 c. Using the steps in (b), answer the following: What are the dimensions of each of the rectangles if the following trinomials represent their product? i. x 2 + 5x + 6 iii. x 2 x - 6 v. x 2 9x + 20 ii. 3x 2 + 3x + 2 iv. x 2 + 7x Consider Activity 2 under Explore.

8 a. How is the side of the square obtained given its area? b. Write the procedure in getting the factors of perfect square trinomial x 2 + 4x + 4? x 2 + 2xy+ y 2? c. Explain how to distinguish perfect square trinomials from other trinomials. Describe the factors of perfect square trinomials. Use the steps in (b) to find the factors of the following: i. x 2 + 6x + 9 iii. p p + 36 v. 16x xy + 9y 2 ii. m m + 25 iv. 9x x Use algebra tiles to verify the given equation: 2 2 a. 4x + 12xy + 9y = ( 2x + 3y) 2 b. 4x 2 4xy + y 2 = (2x y) 2 5. Consider Activity 3 under Explore. a. How do you represent the area of the remaining parts? b. Write the procedure in getting factors of the difference of two squares: x 2 y 2 c. Use the procedure in (b) to factor the following: i. x 2 9 iii. 4x v. 9x 2 4 ii. 9x 2 36 iv. 36x Compare the different ways of factoring. 7. If ( x + y)(x 2 xy + y 2 ) = x 3 + y 3 and ( x y)(x 2 + xy + y 2 ) = x 3 y 3, what are the factors of x 3 + y 3 and x 3 y 3? Use the above ideas in getting the factors of the following: a. a 3 27 c. x e. 125m 3 n 3 8 b. 8x 3 + y 3 d. 64x y 3 3. Deepen Analyze the following problems: 1. If the area of a square garden is (x 2 + 8x + 16) sq units, is it possible to find the measure of its side? Why? Or why not? How?

9 2. If the area of a garden is (3x 2 + 8x + 4) sq units, is it possible to find the measure of the side? Is the garden a square? Why? Or why not? 3. Is x 2 y 2 = (x y) 2? Explain why or why not. If you do not understand the rules on factoring, what do you think will happen? 4. What is the difference of the squares of 105 and 5? What is the square of their difference? 5. Explain or illustrate how you can find the difference of the squares of two terms using 105 and Transfer A. Solve: A box with no top is to be made from an 8 inch by 6 inch piece of metal by cutting identical squares from each corner and turning up the sides. The volume of the box is modeled by the polynomial (4x 3-28x 2 +48x). Find the dimensions of the box. B. 1. Using models, present a problem solving plan that will make use of the concept of factoring. 2. Write a journal about the rules on finding factors of polynomials. Send it to your friend who is studying in a different school through a letter, , etc. Submit a copy of the journal.

### 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 UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can

### 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

### 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

### A Concrete Introduction. to the Abstract Concepts. of Integers and Algebra using Algebra Tiles A Concrete Introduction to the Abstract Concepts of Integers and Algebra using Algebra Tiles Table of Contents Introduction... 1 page Integers 1: Introduction to Integers... 3 2: Working with Algebra Tiles...

### 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.

### 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.

### 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

### 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

### 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

### 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

### 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

### 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

### ( ) 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

### TEACHING GUIDE. The learner demonstrates understanding of the key concepts of special products and factors of polynomials. TEACHING GUIDE Module 1: Special products and Factors A. Learning Outcomes 1. Grade Level Standard The learner demonstrates understanding of key concepts and principles of algebra, geometry, probability

### 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

### SOL Warm-Up Graphing Calculator Active A.2a (a) Using laws of exponents to simplify monomial expressions and ratios of monomial expressions 1. Which expression is equivalent to (5x 2 )(4x 5 )? A 9x 7 B 9x 10 C 20x 7 D 20x 10 2. Which expression

### 7-2 Factoring by GCF. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1 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, Solving. Equations, and Problem Solving REVISED PAGES 05-W4801-AM1.qxd 8/19/08 8:45 PM Page 241 Factoring, Solving Equations, and Problem Solving 5 5.1 Factoring by Using the Distributive Property 5.2 Factoring the Difference of Two Squares 5.3 Factoring

### 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

### 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

### 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

### Factoring. Factoring Polynomial Equations. Special Factoring Patterns. Factoring. Special Factoring Patterns. Special Factoring Patterns Factoring Factoring Polynomial Equations Ms. Laster Earlier, you learned to factor several types of quadratic expressions: General trinomial - 2x 2-5x-12 = (2x + 3)(x - 4) Perfect Square Trinomial - x

### 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

### 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

### 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/

### Factor Polynomials Completely 9.8 Factor Polynomials Completely Before You factored polynomials. Now You will factor polynomials completely. Why? So you can model the height of a projectile, as in Ex. 71. Key Vocabulary factor by grouping

### Factor and Solve Polynomial Equations. In Chapter 4, you learned how to factor the following types of quadratic expressions. 5.4 Factor and Solve Polynomial Equations Before You factored and solved quadratic equations. Now You will factor and solve other polynomial equations. Why? So you can find dimensions of archaeological

### 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

### CPM Educational Program CPM Educational Program A California, Non-Profit Corporation Chris Mikles, National Director (888) 808-4276 e-mail: mikles @cpm.org CPM Courses and Their Core Threads Each course is built around a few

### 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 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 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

### 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 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

### 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 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

### SPECIAL PRODUCTS AND FACTORS SPECIAL PRODUCTS AND FACTORS I. INTRODUCTION AND FOCUS QUESTIONS http://dmciresidences.com/home/20/0/ cedar-crest-condominiums/ http://frontiernerds.com/metal-box http://mazharalticonstruction.blogspot.

### Section A-3 Polynomials: Factoring APPLICATIONS. A-22 Appendix A A BASIC ALGEBRA REVIEW A- Appendi A A BASIC ALGEBRA REVIEW C In Problems 53 56, perform the indicated operations and simplify. 53. ( ) 3 ( ) 3( ) 4 54. ( ) 3 ( ) 3( ) 7 55. 3{[ ( )] ( )( 3)} 56. {( 3)( ) [3 ( )]} 57. Show by

### Lesson 9.1 Solving Quadratic Equations Lesson 9.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with a. One -intercept and all nonnegative y-values. b. The verte in the third quadrant and no -intercepts. c. The verte

### Polynomials. Key Terms. quadratic equation parabola conjugates trinomial. polynomial coefficient degree monomial binomial GCF Polynomials 5 5.1 Addition and Subtraction of Polynomials and Polynomial Functions 5.2 Multiplication of Polynomials 5.3 Division of Polynomials Problem Recognition Exercises Operations on Polynomials

### 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

### Mathematics More Visual Using Algebra Tiles www.cpm.org Chris Mikles CPM Educational Program A California Non-profit Corporation 33 Noonan Drive Sacramento, CA 958 (888) 808-76 fa: (08) 777-8605 email: mikles@cpm.org An Eemplary Mathematics Program

### 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

### 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

### 6706_PM10SB_C4_CO_pp192-193.qxd 5/8/09 9:53 AM Page 192 192 NEL 92 NEL Chapter 4 Factoring Algebraic Epressions GOALS You will be able to Determine the greatest common factor in an algebraic epression and use it to write the epression as a product Recognize different

### 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

### 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

### In this section, you will develop a method to change a quadratic equation written as a sum into its product form (also called its factored form). CHAPTER 8 In Chapter 4, you used a web to organize the connections you found between each of the different representations of lines. These connections enabled you to use any representation (such as a graph,

### MATH 102 College Algebra FACTORING Factoring polnomials ls is simpl the reverse process of the special product formulas. Thus, the reverse process of special product formulas will be used to factor polnomials. To factor polnomials

### Learning Objectives 9.2. Media Run Times 9.3 Unit 9 Table of Contents Unit 9: Factoring Video Overview Learning Objectives 9.2 Media Run Times 9.3 Instructor Notes 9.4 The Mathematics of Factoring Polynomials Teaching Tips: Conceptual Challenges

### 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.

### Online EFFECTIVE AS OF JANUARY 2013 2013 A and C Session Start Dates (A-B Quarter Sequence*) 2013 B and D Session Start Dates (B-A Quarter Sequence*) Quarter 5 2012 1205A&C Begins November 5, 2012 1205A Ends December 9, 2012 Session Break

### 6.1 Add & Subtract Polynomial Expression & Functions 6.1 Add & Subtract Polynomial Expression & Functions Objectives 1. Know the meaning of the words term, monomial, binomial, trinomial, polynomial, degree, coefficient, like terms, polynomial funciton, quardrtic

### SECTION A-3 Polynomials: Factoring A-3 Polynomials: Factoring A-23 thick, write an algebraic epression in terms of that represents the volume of the plastic used to construct the container. Simplify the epression. [Recall: The volume 4

### 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

### MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 17, 2006 MTH 092 College Algebra Essex County College Division of Mathematics Sample Review Questions Created January 7, 2006 Math 092, Elementary Algebra, covers the mathematical content listed below. In order

### 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

### 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

### 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,

### POLYNOMIAL FUNCTIONS POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a

### Math 10C. Course: Polynomial Products and Factors. Unit of Study: Step 1: Identify the Outcomes to Address. Guiding Questions: Course: Unit of Study: Math 10C Polynomial Products and Factors Step 1: Identify the Outcomes to Address Guiding Questions: What do I want my students to learn? What can they currently understand and do?

### 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 - Factoring Special Products 6.5 Factoring - Factoring Special Products Objective: Identify and factor special products including a difference of squares, perfect squares, and sum and difference of cubes. When factoring there are

### 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!

### Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. Algebra 2 - Chapter Prerequisites Vocabulary Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. P1 p. 1 1. counting(natural) numbers - {1,2,3,4,...}

### 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)

### 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

### 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

### Learning Objectives 8.2. Media Run Times 8.3. Instructor Overview 8.8 Tutor Simulation: Roman Numerals and Polynomials Unit 8 Table of Contents Unit 8: Polynomials Video Overview Learning Objectives 8.2 Media Run Times 8.3 Instructor Notes 8.4 The Mathematics of Monomials and Polynomials Teaching Tips: Conceptual Challenges

### called and explain why it cannot be factored with algebra tiles? and explain why it cannot be factored with algebra tiles? Factoring Reporting Category Topic Expressions and Operations Factoring polynomials Primary SOL A.2c The student will perform operations on polynomials, including factoring completely first- and second-degree

### Multiplying Binomials and Factoring Trinomials Using Algebra Tiles and Generic Rectangles Multiplying Binomials Standard: Algebra 10.0 Time: 55 mins. Multiplying Binomials and Factoring Trinomials Using Algebra Tiles and s Materials: Class set of Algebra Tiles or access to a computer for each

### Unit 3: Day 2: Factoring Polynomial Expressions Unit 3: Day : Factoring Polynomial Expressions Minds On: 0 Action: 45 Consolidate:10 Total =75 min Learning Goals: Extend knowledge of factoring to factor cubic and quartic expressions that can be factored

### 10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED CONDENSED L E S S O N 10.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations

### Chris Yuen. Algebra 1 Factoring. Early High School 8-10 Time Span: 5 instructional days 1 Chris Yuen Algebra 1 Factoring Early High School 8-10 Time Span: 5 instructional days Materials: Algebra Tiles and TI-83 Plus Calculator. AMSCO Math A Chapter 18 Factoring. All mathematics material and

### 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,

### 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

### 1.1 Practice Worksheet Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c) 476 CHAPTER 7 Graphs, Equations, and Inequalities 7. Quadratic Equations Now Work the Are You Prepared? problems on page 48. OBJECTIVES 1 Solve Quadratic Equations by Factoring (p. 476) Solve Quadratic

### Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics

### 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

### Mathematics Georgia Performance Standards Mathematics Georgia Performance Standards K-12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by

### 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.

### CM2202: Scientific Computing and Multimedia Applications General Maths: 2. Algebra - Factorisation CM2202: Scientific Computing and Multimedia Applications General Maths: 2. Algebra - Factorisation Prof. David Marshall School of Computer Science & Informatics Factorisation Factorisation is a way of

### Algebra I Vocabulary Cards Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

### 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

### PERFECT SQUARES AND FACTORING EXAMPLES PERFECT SQUARES AND FACTORING EXAMPLES 1. Ask the students what is meant by identical. Get their responses and then explain that when we have two factors that are identical, we call them perfect squares.

### BEGINNING ALGEBRA ACKNOWLEDMENTS BEGINNING ALGEBRA The Nursing Department of Labouré College requested the Department of Academic Planning and Support Services to help with mathematics preparatory materials for its Bachelor of Science

### Factoring. 472 Chapter 9 Factoring Factoring Lesson 9- Find the prime factorizations of integers and monomials. Lesson 9- Find the greatest common factors (GCF) for sets of integers and monomials. Lessons 9-2 through 9-6 Factor polynomials.

### Mathematics Curriculum Common Core Mathematics Curriculum Table of Contents 1 Polynomial and Quadratic Expressions, Equations, and Functions MODULE 4 Module Overview... 3 Topic A: Quadratic Expressions, Equations, Functions,

### Mathematics Online Instructional Materials Correlation to the 2009 Algebra I Standards of Learning and Curriculum Framework Provider York County School Division Course Syllabus URL http://yorkcountyschools.org/virtuallearning/coursecatalog.aspx Course Title Algebra I AB Last Updated 2010 - A.1 The student will represent verbal

### 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,

### 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

### Finding Solutions of Polynomial Equations DETAILED SOLUTIONS AND CONCEPTS - POLYNOMIAL EQUATIONS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! PLEASE NOTE Name Class Date 6.4 Factoring Polynomials Essential Question: What are some ways to factor a polynomial, and how is factoring useful? Resource Locker Explore Analyzing a Visual Model for Polynomial Factorization Sheets Algebra Cheat Sheets provide you with a tool for teaching your students note-taking, problem-solving, and organizational skills in the context of algebra lessons. These sheets teach the concepts