CHAPTER 7: FACTORING POLYNOMIALS


 Valerie Daniel
 4 years ago
 Views:
Transcription
1 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 an epression is to rewrite it as a product of or more quantities. Factoring is sometimes called FACTORIZATION. 1 can be FACTORED into the product 3*. Variable Epressions can also be factored. 3 can be factored into 7( ) or (7) or (7 ), etc How about this polnomial epression? To factor a polnomial, the FIRST STEP is to look for a GREATEST COMMON FACTOR. The GCF of a polnomial is the GREATEST number (or variable epression) that is a factor of ever term in the epression. That is, it is the variable epression that is the GCF of the coefficients, and the GCF of each of the variables. How man terms are there? What are the? What is the GCF of these terms? Let s take another look at the polnomial: Coefficients: The Coefficients are, 3, and 10. The Coefficient GCF is. Variables: The onl variable is, the first term has 3, the nd term has, the third term has. The GCF is the greatest power that can go into ALL of those terms, but practicall this means it will be the variable term with the smallest power: The GCF of is Now to factor the polnomial: Rewrite the polnomial as a product with as one factor, and the remaining epression (after dividing each term b ) This polnomial cannot be factored an more. It is prime. We ll see wh later.
2 GCF :,, : ' GCF :,, : ' GCF : 1 Coefficients :16,8, and Eample: s s Put it all together and the GCF of the polnomial is: NOW YOU TRY: Factor this:
3 Tr factoring 3() () FACTORING BY GROUPING Eample: ( + ) + 3( + ) Remember, a FACTOR is something being multiplied in a product. Do ou see a common factor in this epression? ( + ) + 3( + ) COMMON FACTOR ( ) ( ) ( )( 3) 3( ) Eample : (  ) + (  ) At first, it looks like there is no common factor, but notice that  and  are ver similar. In fact,  () = + =  So we can rewrite () has () (  ) + ((  )) = (  ) (  ) =( )( )
4 Eample : If there is not a common factor of ALL the terms, ou can factor b GROUPING the terms in to groups that DO have a common factor. (3 3 ) + ( 6 + 8) = (3  ) + (3 ) Factor out a  instead of so that this group will have a common factor to the other group (3 ). = (3  )( ) YOU TRY FACTORING
5 FACTORING POLYNOMIALS OF THE FORM + b + c Eample 1: Factor the polnomial: STEP 1: Is there a GCF of all three terms? NO STEP : Is this polnomial a trinomial with degree? YES Since this is a trinomial with degree, it is possible that this polnomial can be factored into binomials: ( + a )( + b ) Remember, the FOIL method for ( + a)( + b) = + a + b + ab = + (a + b) + ab So from this general form, we see that the factors of the Last Term (ab), must add up to make the Middle Term s coefficient. STEP 3: Tr different factor s of the Last Term that will add up to the Middle Term s coefficient. Polnomial: Last Term: Middle Term s Coefficient: Factors of Last Term Sum of Those Factors 1, = 33,8 +8 = 1, = 18 FACTORIZATION: ( + )( + 16)
6 Eample : Factor 6 16 STEP 1: Is there a GCF of all three terms? STEP : Is it a trinomial with degree? Last Term: Middle Term s Coefficient: Factors of Last Term Sum of Those Factors 1, = 11, = 1, = 6 , = 6, = 0 ,  + = 0 FACTORIZATION: ( )( +8) UNFACTORABLE TRINOMIALS: 6 8 There are no factors of 8 that can add up to 6, So this is considered a prime polnomial and is nonfactorable over the integers.
7 Eample: Factor 3a b 18ab 81b STEP 1: Is there a GCF of all three terms? YES GCF is Factor out the GCF: STEP : After factoring out the GCF is one of the factors a trinomial with degree? STEP 3: Find factors of the last term of the trinomial that add up to the middle term s coefficient and factor into two binomials. STEP : Don t forget STEP 1 S GCF in ou final factorization!
8 EXAMPLE : Factor STEP 1: Is there a GCF of all terms? NO STEP : Is this a trinomial with degree? YES STEP 3: Find factors of the last term of the trinomial that add up to the middle term s coefficient and factor into two binomials. In this case, make sure the factors of the the last term are like terms that can be combined. (eg. 0 and 1 are not like terms but are factors of 0 ) Factors of Last Term, 0 Sum of Those Factors 0, =1, = 1, + = 9 FACTORIZATION: ( + )( + )
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.
More informationChapter 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
More information1.3 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.
More informationFactoring 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
More informationPreCalculus 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...
More informationSection 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
More informationGreatest 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
More informationNSM100 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
More informationFactoring 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
More informationWe start with the basic operations on polynomials, that is adding, subtracting, and multiplying.
R. Polnomials In this section we want to review all that we know about polnomials. We start with the basic operations on polnomials, that is adding, subtracting, and multipling. Recall, to add subtract
More informationFACTORING 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
More informationWhen 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
More informationThe 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
More informationPolynomials 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
More informationIn algebra, factor by rewriting a polynomial as a product of lowerdegree 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
More information5 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
More informationFACTORING 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".
More informationMath 25 Activity 6: Factoring Advanced
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
More informationSimplification 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.
More informationThe 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.
More informationFactoring 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.
More information( ) 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
More informationFactoring 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
More informationFactoring. 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,
More informationexpression 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
More informationa. 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
More informationFactoring (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
More informationSUNY ECC. ACCUPLACER Preparation Workshop. Algebra Skills
SUNY ECC ACCUPLACER Preparation Workshop Algebra Skills Gail A. Butler Ph.D. Evaluating Algebraic Epressions Substitute the value (#) in place of the letter (variable). Follow order of operations!!! E)
More information6.3 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
More information6.4 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
More informationx 41 = (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) =
More informationA. 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!
More informationFactoring 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
More informationFactoring 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
More informationFactoring 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,
More informationThis 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 byncsa 3.0 (http://creativecommons.org/licenses/byncsa/
More informationEAP/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
More informationFactoring 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
More informationFACTORING 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
More informationDefinitions 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
More informationAdding 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
More informationFACTORING ax 2 bx c. Factoring Trinomials with Leading Coefficient 1
5.7 Factoring ax 2 bx c (549) 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.
More informationAIP 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
More informationName 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
More informationA.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
More informationBy 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
More informationFactors 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
More informationFactoring 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
More informationFactoring 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
More information15.1 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
More informationChapter 3 Section 6 Lesson Polynomials
Chapter Section 6 Lesson Polynomials Introduction This lesson introduces polynomials and like terms. As we learned earlier, a monomial is a constant, a variable, or the product of constants and variables.
More informationTool 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
More informationFACTORING POLYNOMIALS
296 (540) 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
More information6.6 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
More informationFactoring 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
More informationFACTORING QUADRATICS 8.1.1 through 8.1.4
Chapter 8 FACTORING QUADRATICS 8.. through 8..4 Chapter 8 introduces students to rewriting quadratic epressions and solving quadratic equations. Quadratic functions are any function which can be rewritten
More informationFactoring 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
More informationFactoring 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
More informationAnswers 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
More informationOperations 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
More informationFactoring 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
More informationFactoring 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
More informationSection 5.0A Factoring Part 1
Section 5.0A Factoring Part 1 I. Work Together A. Multiply the following binomials into trinomials. (Write the final result in descending order, i.e., a + b + c ). ( 7)( + 5) ( + 7)( + ) ( + 7)( + 5) (
More informationMATH 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
More informationFactoring 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
More informationAlum 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
More information76. Choosing a Factoring Model. Extension: Factoring Polynomials with More Than One Variable IN T RO DUC E T EACH. Standards for Mathematical Content
76 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
More informationAlgebra 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
More informationFactor 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
More informationSECTION P.5 Factoring Polynomials
BLITMCPB.QXP.0599_4874 /0/0 0:4 AM Page 48 48 Chapter P Prerequisites: Fundamental Concepts of Algebra Technology Eercises Critical Thinking Eercises 98. The common cold is caused by a rhinovirus. The
More informationPrime Factorization, Greatest Common Factor (GCF), and Least Common Multiple (LCM)
Prime Factorization, Greatest Common Factor (GCF), and Least Common Multiple (LCM) Definition of a Prime Number A prime number is a whole number greater than 1 AND can only be divided evenly by 1 and itself.
More information4.4 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
More informationIn 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,
More informationA 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
More informationSECTION 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
More informationTHE POWER RULES. Raising an Exponential Expression to a Power
8 (5) Chapter 5 Eponents and Polnomials 5. THE POWER RULES In this section Raising an Eponential Epression to a Power Raising a Product to a Power Raising a Quotient to a Power Variable Eponents Summar
More informationUnit 6: Polynomials. 1 Polynomial Functions and End Behavior. 2 Polynomials and Linear Factors. 3 Dividing Polynomials
Date Period Unit 6: Polynomials DAY TOPIC 1 Polynomial Functions and End Behavior Polynomials and Linear Factors 3 Dividing Polynomials 4 Synthetic Division and the Remainder Theorem 5 Solving Polynomial
More information2x 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
More informationRational Expressions  Complex Fractions
7. Rational Epressions  Comple Fractions Objective: Simplify comple fractions by multiplying each term by the least common denominator. Comple fractions have fractions in either the numerator, or denominator,
More informationPOLYNOMIALS 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
More informationHigher. Polynomials and Quadratics 64
hsn.uk.net Higher Mathematics UNIT OUTCOME 1 Polnomials and Quadratics Contents Polnomials and Quadratics 64 1 Quadratics 64 The Discriminant 66 3 Completing the Square 67 4 Sketching Parabolas 70 5 Determining
More informationName 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
More information5.1 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.
More informationCopy 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,...}
More informationAcademic Success Centre
250) 9606367 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
More information72 Factoring by GCF. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1
72 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
More information10 7, 8. 2. 6x + 30x + 36 SOLUTION: 89 Perfect Squares. The first term is not a perfect square. So, 6x + 30x + 36 is not a perfect square trinomial.
Squares Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it. 1.5x + 60x + 36 SOLUTION: The first term is a perfect square. 5x = (5x) The last term is a perfect
More information6706_PM10SB_C4_CO_pp192193.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
More informationSect 6.7  Solving Equations Using the Zero Product Rule
Sect 6.7  Solving Equations Using the Zero Product Rule 116 Concept #1: Definition of a Quadratic Equation A quadratic equation is an equation that can be written in the form ax 2 + bx + c = 0 (referred
More informationFactoring 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
More informationMATH 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
More informationReview of Intermediate Algebra Content
Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6
More informationFive 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.
More informationMath 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
More informationIntroduction Assignment
PRECALCULUS 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
More informationSect. 1.3: Factoring
Sect. 1.3: Factoring MAT 109, Fall 2015 Tuesday, 1 September 2015 Algebraic epression review Epanding algebraic epressions Distributive property a(b + c) = a b + a c (b + c) a = b a + c a Special epansion
More informationDeterminants 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
More information