Completing the Square. A trinomial that is the square of a binomial. x Squaring half the coefficient of x. AA65.pdf.
|
|
- Erik Patterson
- 6 years ago
- Views:
Transcription
1 AA65.pdf 6.5 Completing the Square 1. Converting from vertex form to standard form involves expanding the square of the binomial, distributing a, and then isolating y. What method does converting from standard form to vertex form use? Completing the Square y k = a(x h) 2 to y = ax 2 + bx + c (Vertex form) (Standard form) 2. What is a perfect square trinomial? A trinomial that is the square of a binomial 3. Draw a picture of (x + h) 2 = x 2 + 2hx + h 2 Squaring half the coefficient of x. 4. Study example 1 5. Now try the following problem in your notes: a. What number should be added to x 2 + 5x to make a perfect square trinomial? Draw a picture to represent x 2 + 5x.?? x 2.5? 2.5? x Dec 9 9:28 AM 1
2 6. Theorem about completing the square. 7. Study example 2 8. Now try the following problem in your notes: a. Rewrite the equation below in vertex form: i. y = x x + 90 y k = a(x h) 2 1. Rewrite with all x terms alone on one side of the equation y = x x If a = 1 add to both sides of the equation y 90 = x x The trinomial should now be a perfect square trinomial. It can be rewritten as a binomial squared. The first term should be x and the second term should be y 9 = x x + 81 y 9 = (x + 9) 2 Using the calculator we can find the vertex. The value of a will be the same as the value of a in the original equation. k = 9, h = 9, a = 1 Dec 9 9:32 AM 2
3 8. Now try the following problem in your notes: a. Rewrite the equation below in vertex form: y = x 2 11x + 4 ii. y = x 2 11x + 4 y k = a(x h) 2 Rewrite with the x terms alone on one side of the equation y = x 2 11x x x If a = 1 add y 4 = x 2 11x or to both sides of the equation The trinomial should then be able to be rewritten as a binomial squared. The first term should be x and the second term should be y = x 2 11x y = (x ) 2 y = (x 5.5) 2 k = 26.25, h = 5.5, a = 1 Using the calculator we can find the vertex. The value of a will be the same as the value of a in the original equation. Dec 9 2:03 PM 3
4 9. Study example Now try the following problem in your notes: a. Rewrite the equation below in vertex form: i. y = 3x 2 12x + 1 y k = a(x h) 2 Rewrite with the x terms alone on one side of the equation y = 3x 2 12x y 1 = 3x 2 12x if a does not equal 1, divide both sides by a y 1 = 3x 2 12x 3 3 Now add to both sides of the equation The trinomial should then be able to be rewritten as a binomial squared. The first term of the binomial should be x and the second term of teh binomial should be In order to get the equation in vertex form multiply both sides by a (clear fractions) Using the calculator we can find the vertex. The value of a will be the same as the value of a in the original equation. k = 11, h = 2, a = 3 Dec 9 9:35 AM 4
5 9. Study example Now try the following problem in your notes: a. Rewrite the equation below in vertex form: ii. y = 5x 2 + 4x 3 y k = a(x h) 2 Rewrite with the x terms alone on one side of the equation y = 5x 2 + 4x y + 3 = 5x 2 + 4x Divide both sides by a y + 3 = 5x 2 + 4x 5 5 Now add to both sides of the equation In order to get the equation in vertex form multiply both sides by a The trinomial should then be able to be rewritten as a binomial squared. The first term should be x and the second term should be Using the calculator we can find the vertex and the value of a will be the same as the value of a in the original equation. y +2.2 = 5(x.4) 2 k = 2.2, h =.4, a = 5 Dec 9 9:35 AM 5
6 y = 5x 2 + 4x 3 Dec 10 10:48 AM 6
7 11. Now try the following problem in your notes: a. Suppose a ball is thrown straight up from a height of 4 feet with an initial velocity of 50 feet per second. What is the maximum height of the ball? h(t) = 16t t + 4 The maximum height of feet is reached seconds after the ball was thrown. Dec 9 9:35 AM 7
8 Determine a value for a and b to make the statement true. x 2 10x + 25 = ( x + a) 2 a = 4x 2 +12x + 9 = ( 2x + a) 2 a = x 2 + bx + 81 = ( x + a) 2 a = b = x 2 +bx = ( x + a) 2 a = b = x 2 8x + b = ( x + a) 2 a = b = x x + b = ( x + a) 2 a = b = Dec 18 8:03 AM 8
9 Notes 6 5 Review: Perfect Square Trinomial is the result of the square of a binomial (x + 11) 2 = x x y = x 2 + 6x + 10 y = x 2 + 6x +? Completing the Square Algebraically To Go From Standard To Vertex Form a = 1 1. Subtract/add the constant to both sides of the equation. 2. Divide the coefficient of the x term by 2 and square it. Then add that number to both sides of the equation. 3. Simplify both sides. (right side of equation should be a binomial squared) 4. Vertex : Jul 30 6:11 PM 9
10 Try: y = x 2 12x Subtract/add the constant to both sides of the equation. 2. Divide the coefficient of the x term by 2 and square it. Then add that number to both sides of the equation. 3. Simplify both sides. (right side of equation should be a binomial squared) 4. Vertex : Jul 30 6:21 PM 10
11 y = 2x 2 20x + 57 Completing the Square Algebraically To Go From Standard To Vertex Form a 1 1. Subtract/add the constant to both sides of the equation. 2. Multiply both sides by the reciprocal of the coefficient of x 2. (don t simplify left side of the equation ) 3. Divide the coefficient of the x term by 2 and square it. Then add that number to both sides of the equation. 4. Simplify the right side of the equation into a binomial squared. Vertex: 5. Multiply both sides of the equation by the reciprocal of the number originally multiplied on the left side. 6. Simplify the left side of the equation. Do not distribute on the right side. Jul 30 6:25 PM 11
12 Try: y = 6x 2 18x 5 Jul 30 6:28 PM 12
13 Mar 6 12:39 PM 13
14 Mar 6 12:39 PM 14
15 Mar 6 12:39 PM 15
16 1. Rewrite with all x terms alone on one side of the equation 2. If a = 1 add to both sides of the equation If a does not equal 1, divide both sides by a now add to both sides of the equation 3. The trinomial should now be a perfect square trinomial. It can be rewritten as a binomial squared. The first term should be x and the second term should be Dec 9 3:57 PM 16
17 1. Rewrite with all x terms alone on one side of the equation 2. If a = 1 add to both sides of the equation If a does not equal 1, divide both sides by a now add to both sides of the equation 3. The trinomial should now be a perfect square trinomial. It can be rewritten as a binomial squared. The first term should be x and the second term should be Dec 9 3:57 PM 17
18 1. Rewrite with all x terms alone on one side of the equation 2. If a = 1 add to both sides of the equation If a does not equal 1, divide both sides by a now add to both sides of the equation 3. The trinomial should now be a perfect square trinomial. It can be rewritten as a binomial squared. The first term should be x and the second term should be Dec 9 3:57 PM 18
19 Dec 9 3:57 PM 19
20 1. Rewrite with all x terms alone on one side of the equation 2. If a = 1 add to both sides of the equation If a does not equal 1, divide both sides by a now add to both sides of the equation 3. The trinomial should now be a perfect square trinomial. It can be rewritten as a binomial squared. The first term should be x and the second term should be Dec 9 3:57 PM 20
21 Dec 9 4:00 PM 21
22 Dec 9 4:01 PM 22
23 Dec 9 4:01 PM 23
24 Dec 9 4:08 PM 24
25 Dec 9 4:01 PM 25
26 Dec 9 4:02 PM 26
27 Dec 9 4:07 PM 27
28 becomes becomes Dec 9 4:02 PM 28
29 Dec 9 4:07 PM 29
30 Dec 9 4:02 PM 30
31 Dec 9 4:04 PM 31
32 Mar 11 1:27 PM 32
33 Mar 11 1:36 PM 33
34 Chapter 6 WS 6 5.pdf Mar 11 1:23 PM 34
35 Dec 8 9:27 AM 35
36 Dec 8 9:27 AM 36
37 Dec 8 9:28 AM 37
38 1. Rewrite with all x terms alone on one side of the equation 2. If a = 1 add to both sides of the equation If a does not equal 1, divide both sides by a now add to both sides of the equation 3. The trinomial should now be a perfect square trinomial. It can be rewritten as a binomial squared. The first term should be x and the second term should be Dec 8 9:28 AM 38
39 Dec 8 9:28 AM 39
40 Dec 8 9:28 AM 40
41 Dec 8 9:28 AM 41
42 Dec 8 9:28 AM 42
43 Dec 8 9:28 AM 43
44 Dec 8 9:28 AM 44
45 Dec 8 9:28 AM 45
46 Dec 8 9:25 AM 46
47 Dec 9 9:31 AM 47
48 Attachments AA65.pdf Chapter 6 WS 6 5.pdf
Completing the Square. A trinomial that is the square of a binomial. x Square half the coefficient of x. AA65.pdf.
AA65.pdf 6.5 Completing the Square 1. Converting from vertex form to standard form involves expanding the square of the binomial, distributing a, and then isolating y. What method does converting from
More information2-4 Completing the Square
2-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Write each expression as a trinomial. 1. (x 5) 2 x 2 10x + 25 2. (3x + 5) 2 9x 2 + 30x + 25 Factor each expression. 3.
More informationUNIT 5 QUADRATIC FUNCTIONS Lesson 2: Creating and Solving Quadratic Equations in One Variable Instruction
Prerequisite Skills This lesson requires the use of the following skills: multiplying polynomials working with complex numbers Introduction 2 b 2 A trinomial of the form x + bx + that can be written as
More informationPolynomial and Rational Expressions. College Algebra
Polynomial and Rational Expressions College Algebra Polynomials A polynomial is an expression that can be written in the form a " x " + + a & x & + a ' x + a ( Each real number a i is called a coefficient.
More information8-4 Factoring ax 2 + bx + c. (3x + 2)(2x + 5) = 6x x + 10
When you multiply (3x + 2)(2x + 5), the coefficient of the x 2 -term is the product of the coefficients of the x-terms. Also, the constant term in the trinomial is the product of the constants in the binomials.
More informationWhen Is Factoring Used?
When Is Factoring Used? Name: DAY 9 Date: 1. Given the function, y = x 2 complete the table and graph. x y 2 1 0 1 2 3 1. A ball is thrown vertically upward from the ground according to the graph below.
More informationFactor Trinomials When the Coefficient of the Second-Degree Term is 1 (Objective #1)
Factoring Trinomials (5.2) Factor Trinomials When the Coefficient of the Second-Degree Term is 1 EXAMPLE #1: Factor the trinomials. = = Factor Trinomials When the Coefficient of the Second-Degree Term
More informationIs the following a perfect cube? (use prime factorization to show if it is or isn't) 3456
Is the following a perfect cube? (use prime factorization to show if it is or isn't) 3456 Oct 2 1:50 PM 1 Have you used algebra tiles before? X 2 X 2 X X X Oct 3 10:47 AM 2 Factor x 2 + 3x + 2 X 2 X X
More informationSlide 1 / 128. Polynomials
Slide 1 / 128 Polynomials Slide 2 / 128 Table of Contents Factors and GCF Factoring out GCF's Factoring Trinomials x 2 + bx + c Factoring Using Special Patterns Factoring Trinomials ax 2 + bx + c Factoring
More informationHow can we factor polynomials?
How can we factor polynomials? Factoring refers to writing something as a product. Factoring completely means that all of the factors are relatively prime (they have a GCF of 1). Methods of factoring:
More informationFactoring Quadratic Expressions VOCABULARY
5-5 Factoring Quadratic Expressions TEKS FOCUS Foundational to TEKS (4)(F) Solve quadratic and square root equations. TEKS (1)(C) Select tools, including real objects, manipulatives, paper and pencil,
More informationWe can solve quadratic equations by transforming the. left side of the equation into a perfect square trinomial
Introduction We can solve quadratic equations by transforming the left side of the equation into a perfect square trinomial and using square roots to solve. Previously, you may have explored perfect square
More informationa*(variable) 2 + b*(variable) + c
CH. 8. Factoring polynomials of the form: a*(variable) + b*(variable) + c Factor: 6x + 11x + 4 STEP 1: Is there a GCF of all terms? NO STEP : How many terms are there? Is it of degree? YES * Is it in the
More informationUnit 8: Quadratic Expressions (Polynomials)
Name: Period: Algebra 1 Unit 8: Quadratic Expressions (Polynomials) Note Packet Date Topic/Assignment HW Page Due Date 8-A Naming Polynomials and Combining Like Terms 8-B Adding and Subtracting Polynomials
More informationTool 1. Greatest Common Factor (GCF)
Chapter 7: 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 Simple Trinomials February 24, What's Going On? What's the Pattern? Working Backwards. Finding Factors
What's Going On? What's the Pattern? Working Backwards Finding Factors Learning Goal I will be able to factor standard form equations when a = 1. What's the Pattern? (x + 2)(x + 3) = x 2 + 5x + 6 (x +
More informationSection 13.1 The Greatest Common Factor and Factoring by Grouping. to continue. Also, circle your answer to each numbered exercise.
Algebra Foundations First Edition, Elayn Martin-Gay Sec. 13.1 Section 13.1 The Greatest Common Factor and Factoring by Grouping Complete the outline as you view Video Lecture 13.1. Pause the video as needed
More informationAlg2A Factoring and Equations Review Packet
1 Factoring using GCF: Take the greatest common factor (GCF) for the numerical coefficient. When choosing the GCF for the variables, if all the terms have a common variable, take the one with the lowest
More information3.1 Factors and Multiples of Whole Numbers
3.1 Factors and Multiples of Whole Numbers LESSON FOCUS: Determine prime factors, greatest common factors, and least common multiples of whole numbers. The prime factorization of a natural number is the
More informationMATH 181-Quadratic Equations (7 )
MATH 181-Quadratic Equations (7 ) 7.1 Solving a Quadratic Equation by Factoring I. Factoring Terms with Common Factors (Find the greatest common factor) a. 16 1x 4x = 4( 4 3x x ) 3 b. 14x y 35x y = 3 c.
More information9/16/ (1) Review of Factoring trinomials. (2) Develop the graphic significance of factors/roots. Math 2 Honors - Santowski
(1) Review of Factoring trinomials (2) Develop the graphic significance of factors/roots (3) Solving Eqn (algebra/graphic connection) 1 2 To expand means to write a product of expressions as a sum or difference
More informationAlgebra 7-4 Study Guide: Factoring (pp & 487) Page 1! of 11!
Page 1! of 11! Attendance Problems. Find each product. 1.(x 2)(2x + 7) 2. (3y + 4)(2y + 9) 3. (3n 5)(n 7) Factor each trinomial. 4. x 2 +4x 32 5. z 2 + 15z + 36 6. h 2 17h + 72 I can factor quadratic trinomials
More informationCCAC ELEMENTARY ALGEBRA
CCAC ELEMENTARY ALGEBRA Sample Questions TOPICS TO STUDY: Evaluate expressions Add, subtract, multiply, and divide polynomials Add, subtract, multiply, and divide rational expressions Factor two and three
More informationFactoring is the process of changing a polynomial expression that is essentially a sum into an expression that is essentially a product.
Ch. 8 Polynomial Factoring Sec. 1 Factoring is the process of changing a polynomial expression that is essentially a sum into an expression that is essentially a product. Factoring polynomials is not much
More informationUniversity of Phoenix Material
1 University of Phoenix Material Factoring and Radical Expressions The goal of this week is to introduce the algebraic concept of factoring polynomials and simplifying radical expressions. Think of factoring
More informationChapter 6: Quadratic Functions & Their Algebra
Chapter 6: Quadratic Functions & Their Algebra Topics: 1. Quadratic Function Review. Factoring: With Greatest Common Factor & Difference of Two Squares 3. Factoring: Trinomials 4. Complete Factoring 5.
More informationFactoring completely is factoring a product down to a product of prime factors. 24 (2)(12) (2)(2)(6) (2)(2)(2)(3)
Factoring Contents Introduction... 2 Factoring Polynomials... 4 Greatest Common Factor... 4 Factoring by Grouping... 5 Factoring a Trinomial with a Table... 5 Factoring a Trinomial with a Leading Coefficient
More information(2/3) 3 ((1 7/8) 2 + 1/2) = (2/3) 3 ((8/8 7/8) 2 + 1/2) (Work from inner parentheses outward) = (2/3) 3 ((1/8) 2 + 1/2) = (8/27) (1/64 + 1/2)
Exponents Problem: Show that 5. Solution: Remember, using our rules of exponents, 5 5, 5. Problems to Do: 1. Simplify each to a single fraction or number: (a) ( 1 ) 5 ( ) 5. And, since (b) + 9 + 1 5 /
More informationSection 6.3 Multiplying & Dividing Rational Expressions
Section 6.3 Multiplying & Dividing Rational Expressions MULTIPLYING FRACTIONS In arithmetic, we can multiply fractions by multiplying the numerators separately from the denominators. For example, multiply
More informationAccuplacer Review Workshop. Intermediate Algebra. Week Four. Includes internet links to instructional videos for additional resources:
Accuplacer Review Workshop Intermediate Algebra Week Four Includes internet links to instructional videos for additional resources: http://www.mathispower4u.com (Arithmetic Video Library) http://www.purplemath.com
More informationFactoring is the process of changing a polynomial expression that is essentially a sum into an expression that is essentially a product.
Ch. 8 Polynomial Factoring Sec. 1 Factoring is the process of changing a polynomial expression that is essentially a sum into an expression that is essentially a product. Factoring polynomials is not much
More informationSection 7.4 Additional Factoring Techniques
Section 7.4 Additional Factoring Techniques Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Factor trinomials when a = 1. Multiplying binomials
More informationQuadratic Algebra Lesson #2
Quadratic Algebra Lesson # Factorisation Of Quadratic Expressions Many of the previous expansions have resulted in expressions of the form ax + bx + c. Examples: x + 5x+6 4x 9 9x + 6x + 1 These are known
More informationSkills Practice Skills Practice for Lesson 10.1
Skills Practice Skills Practice for Lesson 10.1 Name Date Water Balloons Polynomials and Polynomial Functions Vocabulary Match each key term to its corresponding definition. 1. A polynomial written with
More informationMath 1201 Unit 3 Factors and Products Final Review. Multiple Choice. 1. Factor the binomial. a. c. b. d. 2. Factor the binomial. a. c. b. d.
Multiple Choice 1. Factor the binomial. 2. Factor the binomial. 3. Factor the trinomial. 4. Factor the trinomial. 5. Factor the trinomial. 6. Factor the trinomial. 7. Factor the binomial. 8. Simplify the
More informationWeek 20 Algebra 1 Assignment:
Week 0 Algebra 1 Assignment: Day 1: pp. 38-383 #-0 even, 3-7 Day : pp. 385-386 #-18 even, 1-5 Day 3: pp. 388-389 #-4 even, 7-9 Day 4: pp. 39-393 #1-37 odd Day 5: Chapter 9 test Notes on Assignment: Pages
More informationElementary Algebra Review for Exam 3
Elementary Algebra Review for Exam ) After receiving a discount of 5% on its bulk order of typewriter ribbons, John's Office Supply pays $5882. What was the price of the order before the discount? Round
More informationAdding and Subtracting Rational Expressions
Adding and Subtracting Rational Expressions To add or subtract rational expressions, follow procedures similar to those used in adding and subtracting rational numbers. 4 () 4(3) 10 1 3 3() (3) 1 1 1 All
More informationMath 101, Basic Algebra Author: Debra Griffin
Math 101, Basic Algebra Author: Debra Griffin Name Chapter 5 Factoring 5.1 Greatest Common Factor 2 GCF, factoring GCF, factoring common binomial factor 5.2 Factor by Grouping 5 5.3 Factoring Trinomials
More informationChapter 6.1: Introduction to parabolas and solving equations by factoring
Chapter 6 Solving Quadratic Equations and Factoring Chapter 6.1: Introduction to parabolas and solving equations by factoring If you push a pen off a table, how does it fall? Does it fall like this? Or
More information(x + 3) 2 = (x + 3)(x + 3) = x 2 + 3x + 3x + 9 = x 2 + 6x + 9 Perfect Square Trinomials
Perfect Square Trinomials Perfect Square Trinomials are trinomials that have: 1. a product (ax 2 + bx + c) that is a perfect square 2. a sum that has the same factors of the product when added together
More informationP.1 Algebraic Expressions, Mathematical models, and Real numbers. Exponential notation: Definitions of Sets: A B. Sets and subsets of real numbers:
P.1 Algebraic Expressions, Mathematical models, and Real numbers If n is a counting number (1, 2, 3, 4,..) then Exponential notation: b n = b b b... b, where n is the Exponent or Power, and b is the base
More information2 TERMS 3 TERMS 4 TERMS (Must be in one of the following forms (Diamond, Slide & Divide, (Grouping)
3.3 Notes Factoring Factoring Always look for a Greatest Common Factor FIRST!!! 2 TERMS 3 TERMS 4 TERMS (Must be in one of the following forms (Diamond, Slide & Divide, (Grouping) to factor with two terms)
More informationAlgebra. Chapter 8: Factoring Polynomials. Name: Teacher: Pd:
Algebra Chapter 8: Factoring Polynomials Name: Teacher: Pd: Table of Contents o Day 1: SWBAT: Factor polynomials by using the GCF. Pgs: 1-6 HW: Pages 7-8 o Day 2: SWBAT: Factor quadratic trinomials of
More informationUnit 8 Notes: Solving Quadratics by Factoring Alg 1
Unit 8 Notes: Solving Quadratics by Factoring Alg 1 Name Period Day Date Assignment (Due the next class meeting) Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday Tuesday
More informationMATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 3 (New Material From: , , and 10.1)
NOTE: In addition to the problems below, please study the handout Exercise Set 10.1 posted at http://www.austincc.edu/jbickham/handouts. 1. Simplify: 5 7 5. Simplify: ( ab 5 c )( a c 5 ). Simplify: 4x
More informationGetting Ready for Algebra 2 - Test 3 Review
Getting Ready for Algebra 2 - Test 3 Review Short Answer 1. Simplify the expression. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Simplify the product using FOIL. 15. 16. Find the square. 17. Find the product.
More information-5y 4 10y 3 7y 2 y 5: where y = -3-5(-3) 4 10(-3) 3 7(-3) 2 (-3) 5: Simplify -5(81) 10(-27) 7(9) (-3) 5: Evaluate = -200
Polynomials: Objective Evaluate, add, subtract, multiply, and divide polynomials Definition: A Term is numbers or a product of numbers and/or variables. For example, 5x, 2y 2, -8, ab 4 c 2, etc. are all
More informationName: Algebra Unit 7 Polynomials
Name: Algebra Unit 7 Polynomials Monomial Binomial Trinomial Polynomial Degree Term Standard Form 1 ((2p 3 + 6p 2 + 10p) + (9p 3 + 11p 2 + 3p) TO REMEMBER Adding and Subtracting Polynomials TO REMEMBER
More informationDevelopmental Math An Open Program Unit 12 Factoring First Edition
Developmental Math An Open Program Unit 12 Factoring First Edition Lesson 1 Introduction to Factoring TOPICS 12.1.1 Greatest Common Factor 1 Find the greatest common factor (GCF) of monomials. 2 Factor
More informationSection 7.1 Common Factors in Polynomials
Chapter 7 Factoring How Does GPS Work? 7.1 Common Factors in Polynomials 7.2 Difference of Two Squares 7.3 Perfect Trinomial Squares 7.4 Factoring Trinomials: (x 2 + bx + c) 7.5 Factoring Trinomials: (ax
More informationACCUPLACER Elementary Algebra Assessment Preparation Guide
ACCUPLACER Elementary Algebra Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre
More informationFactoring Trinomials: Part 1
Factoring Trinomials: Part 1 Factoring Trinomials (a = 1) We will now learn to factor trinomials of the form a + b + c, where a = 1 Because a is the coefficient of the leading term of the trinomial, this
More informationPolynomials. Factors and Greatest Common Factors. Slide 1 / 128. Slide 2 / 128. Slide 3 / 128. Table of Contents
Slide 1 / 128 Polynomials Table of ontents Slide 2 / 128 Factors and GF Factoring out GF's Factoring Trinomials x 2 + bx + c Factoring Using Special Patterns Factoring Trinomials ax 2 + bx + c Factoring
More informationMini-Lecture 6.1 The Greatest Common Factor and Factoring by Grouping
Copyright 01 Pearson Education, Inc. Mini-Lecture 6.1 The Greatest Common Factor and Factoring by Grouping 1. Find the greatest common factor of a list of integers.. Find the greatest common factor of
More informationChapter 8: Factoring Polynomials. Algebra 1 Mr. Barr
p. 1 Chapter 8: Factoring Polynomials Algebra 1 Mr. Barr Name: p. 2 Date Schedule Lesson/Activity 8.1 Monomials & Factoring 8.2 Using the Distributive Property 8.3 Quadratics in the form x 2 +bx+c Quiz
More informationPolynomials. Unit 10 Polynomials 2 of 2 SMART Board Notes.notebook. May 15, 2013
Oct 19 9:41 M errick played basketball for 5 out of the 10 days for four hours each. How many hours did errick spend playing basketball? Oct 19 9:41 M Polynomials Polynomials 1 Table of ontents Factors
More informationPOD. Combine these like terms: 1) 3x 2 4x + 5x x 7x ) 7y 2 + 2y y + 5y 2. 3) 5x 4 + 2x x 7x 4 + 3x x
POD Combine these like terms: 1) 3x 2 4x + 5x 2 6 + 9x 7x 2 + 2 2) 7y 2 + 2y 3 + 2 4y + 5y 2 3) 5x 4 + 2x 5 5 10x 7x 4 + 3x 5 12 + 2x 1 Definitions! Monomial: a single term ex: 4x Binomial: two terms separated
More informationTERMINOLOGY 4.1. READING ASSIGNMENT 4.2 Sections 5.4, 6.1 through 6.5. Binomial. Factor (verb) GCF. Monomial. Polynomial.
Section 4. Factoring Polynomials TERMINOLOGY 4.1 Prerequisite Terms: Binomial Factor (verb) GCF Monomial Polynomial Trinomial READING ASSIGNMENT 4. Sections 5.4, 6.1 through 6.5 160 READING AND SELF-DISCOVERY
More informationMATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 3 (New Material From: , , and 10.1)
NOTE: In addition to the problems below, please study the handout Exercise Set 10.1 posted at http://www.austin.cc.tx.us/jbickham/handouts. 1. Simplify: 5 7 5. Simplify: ( 6ab 5 c )( a c 5 ). Simplify:
More informationChapter 4 Factoring and Quadratic Equations
Chapter 4 Factoring and Quadratic Equations Lesson 1: Factoring by GCF, DOTS, and Case I Lesson : Factoring by Grouping & Case II Lesson 3: Factoring by Sum and Difference of Perfect Cubes Lesson 4: Solving
More informationIdentifying & Factoring: x 2 + bx + c
Identifying & Factoring: x 2 + bx + c Apr 13 11:04 AM 1 May 16 8:52 AM 2 A polynomial that can be simplified to the form ax + bx + c, where a 0, is called a quadratic polynomial. Linear term. Quadratic
More informationChapter 5 Polynomials
Department of Mathematics Grossmont College October 7, 2012 Multiplying Polynomials Multiplying Binomials using the Distributive Property We can multiply two binomials using the Distributive Property,
More information7-4 Factoring ax 2 + bx+ c 7-4 Factoring ax 2 +bx+c
7-4 Factoring ax 2 +bx+c Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Find each product. 1. (x 2)(2x + 7) 2. (3y+ 4)(2y + 9) 3. (3n 5)(n 7) 2x 2 + 3x 14 6y 2 + 35y + 36 3n 2 26n+ 35 Find each
More information7.1 Review for Mastery
7.1 Review for Mastery Factors and Greatest Common Factors A prime number has exactly two factors, itself and 1. The number 1 is not a prime number. To write the prime factorization of a number, factor
More informationLesson 7.1: Factoring a GCF
Name Lesson 7.1: Factoring a GCF Date Algebra I Factoring expressions is one of the gateway skills that is necessary for much of what we do in algebra for the rest of the course. The word factor has two
More informationPrerequisites. Introduction CHAPTER OUTLINE
Prerequisites 1 Figure 1 Credit: Andreas Kambanls CHAPTER OUTLINE 1.1 Real Numbers: Algebra Essentials 1.2 Exponents and Scientific Notation 1.3 Radicals and Rational Expressions 1.4 Polynomials 1.5 Factoring
More information1. Which pair of factors of 8 has a sum of 9? 1 and 8 2. Which pair of factors of 30 has a sum of. r 2 4r 45
Warm Up 1. Which pair of factors of 8 has a sum of 9? 1 and 8 2. Which pair of factors of 30 has a sum of 17? 2 and 15 Multiply. 3. (x +2)(x +3) x 2 + 5x + 6 4. (r + 5)(r 9) r 2 4r 45 Objective Factor
More informationMultiply the binomials. Add the middle terms. 2x 2 7x 6. Rewrite the middle term as 2x 2 a sum or difference of terms. 12x 321x 22
Section 5.5 Factoring Trinomials 349 Factoring Trinomials 1. Factoring Trinomials: AC-Method In Section 5.4, we learned how to factor out the greatest common factor from a polynomial and how to factor
More informationSection 13-1: The Distributive Property and Common Factors
Section 13-1: The Distributive Property and Common Factors Factor: 4y 18z 4y 18z 6(4y 3z) Identify the largest factor that is common to both terms. 6 Write the epression as a product by dividing each term
More informationEdexcel past paper questions. Core Mathematics 4. Binomial Expansions
Edexcel past paper questions Core Mathematics 4 Binomial Expansions Edited by: K V Kumaran Email: kvkumaran@gmail.com C4 Binomial Page Binomial Series C4 By the end of this unit you should be able to obtain
More informationDownloaded from
9. Algebraic Expressions and Identities Q 1 Using identity (x - a) (x + a) = x 2 a 2 find 6 2 5 2. Q 2 Find the product of (7x 4y) and (3x - 7y). Q 3 Using suitable identity find (a + 3)(a + 2). Q 4 Using
More informationAlgebra I EOC 10-Day STAAR Review. Hedgehog Learning
Algebra I EOC 10-Day STAAR Review Hedgehog Learning Day 1 Day 2 STAAR Reporting Category Number and Algebraic Methods Readiness Standards 60% - 65% of STAAR A.10(E) - factor, if possible, trinomials with
More informationFACTORISING EQUATIONS
STRIVE FOR EXCELLENCE TUTORING www.striveforexcellence.com.au Factorising expressions with 2 terms FACTORISING EQUATIONS There are only 2 ways of factorising a quadratic with two terms: 1. Look for something
More informationName Class Date. Adding and Subtracting Polynomials
8-1 Reteaching Adding and Subtracting Polynomials You can add and subtract polynomials by lining up like terms and then adding or subtracting each part separately. What is the simplified form of (3x 4x
More information(8m 2 5m + 2) - (-10m 2 +7m 6) (8m 2 5m + 2) + (+10m 2-7m + 6)
Adding Polynomials Adding & Subtracting Polynomials (Combining Like Terms) Subtracting Polynomials (if your nd polynomial is inside a set of parentheses). (x 8x + ) + (-x -x 7) FIRST, Identify the like
More informationAlgebra Module A33. Factoring - 2. Copyright This publication The Northern Alberta Institute of Technology All Rights Reserved.
Algebra Module A33 Factoring - 2 Copyright This publication The Northern Alberta Institute of Technology 2002. All Rights Reserved. LAST REVISED November, 2008 Factoring - 2 Statement of Prerequisite
More informationSection 5.3 Practice Exercises Vocabulary and Key Concepts
Section 5.3 Practice Exercises Vocabulary and Key Concepts 1. a. To multiply 2(4x 5), apply the property. b. The conjugate of 4x + 7 is. c. When two conjugates are multiplied the resulting binomial is
More informationLesson 3 Factoring Polynomials Skills
Lesson 3 Factoring Polynomials Skills I can common factor polynomials. I can factor trinomials like where a is 1. ie. I can factor trinomials where a is not 1. ie. I can factor special products. Common
More information5.1 Exponents and Scientific Notation
5.1 Exponents and Scientific Notation Definition of an exponent a r = Example: Expand and simplify a) 3 4 b) ( 1 / 4 ) 2 c) (0.05) 3 d) (-3) 2 Difference between (-a) r (-a) r = and a r a r = Note: The
More informationFACTORING HANDOUT. A General Factoring Strategy
This Factoring Packet was made possible by a GRCC Faculty Excellence grant by Neesha Patel and Adrienne Palmer. FACTORING HANDOUT A General Factoring Strategy It is important to be able to recognize the
More informationSection 5.5 Factoring Trinomials, a = 1
Section 5.5 Factoring Trinomials, a = 1 REVIEW Each of the following trinomials have a lead coefficient of 1. Let s see how they factor in a similar manner to those trinomials in Section 5.4. Example 1:
More informationSelected Worked Homework Problems. Step 1: The GCF must be taken out first (if there is one) before factoring the hard trinomial.
Section 7 4: Factoring Trinomials of the form Ax 2 + Bx + C with A >1 Selected Worked Homework Problems 1. 2x 2 + 5x + 3 Step 1: The GCF must be taken out first (if there is one) before factoring the hard
More information2.01 Products of Polynomials
2.01 Products of Polynomials Recall from previous lessons that when algebraic expressions are added (or subtracted) they are called terms, while expressions that are multiplied are called factors. An algebraic
More informationWe begin, however, with the concept of prime factorization. Example: Determine the prime factorization of 12.
Chapter 3: Factors and Products 3.1 Factors and Multiples of Whole Numbers In this chapter we will look at the topic of factors and products. In previous years, we examined these with only numbers, whereas
More informationSpecial Factoring Rules
Special Factoring Rules Part of this worksheet deals with factoring the special products covered in Chapter 4, and part of it covers factoring some new special products. If you can identify these special
More informationHFCC Math Lab Beginning Algebra -19. In this handout we will discuss one method of factoring a general trinomial, that is an
HFCC Math Lab Beginning Algebra -19 FACTORING TRINOMIALS a + b+ c ( a In this handout we will discuss one method of factoring a general trinomial, that is an epression of the form a + b+ c where a, b,
More informationName Date
NEW DORP HIGH SCHOOL Deirdre A. DeAngelis, Principal MATHEMATICS DEPARTMENT Li Pan, Assistant Principal Name Date Summer Math Assignment for a Student whose Official Class starts with 7, 8, and 9 Directions:
More informationName Class Date. Multiplying Two Binomials Using Algebra Tiles. 2x(x + 3) = x 2 + x. 1(x + 3) = x +
Name Class Date Multiplying Polynomials Going Deeper Essential question: How do you multiply polynomials? A monomial is a number, a variable, or the product of a number and one or more variables raised
More informationIntegrating rational functions (Sect. 8.4)
Integrating rational functions (Sect. 8.4) Integrating rational functions, p m(x) q n (x). Polynomial division: p m(x) The method of partial fractions. p (x) (x r )(x r 2 ) p (n )(x). (Repeated roots).
More informationChapter 10. Rational Numbers
Chapter 0 Rational Numbers The Histor of Chess 0. Rational Epressions 0. Multipling Rational Epressions 0.3 Dividing Rational Epressions 0. Dividing Polnomials 0.5 Addition and Subtraction of Rational
More informationMTH 110-College Algebra
MTH 110-College Algebra Chapter R-Basic Concepts of Algebra R.1 I. Real Number System Please indicate if each of these numbers is a W (Whole number), R (Real number), Z (Integer), I (Irrational number),
More informationSpecial Binomial Products
Lesson 11-6 Lesson 11-6 Special Binomial Products Vocabulary perfect square trinomials difference of squares BIG IDEA The square of a binomial a + b is the expression (a + b) 2 and can be found by multiplying
More informationUnit 8: Polynomials Chapter Test. Part 1: Identify each of the following as: Monomial, binomial, or trinomial. Then give the degree of each.
Unit 8: Polynomials Chapter Test Part 1: Identify each of the following as: Monomial, binomial, or trinomial. Then give the degree of each. 1. 9x 2 2 2. 3 3. 2x 2 + 3x + 1 4. 9y -1 Part 2: Simplify each
More informationDevelopmental Mathematics Third Edition, Elayn Martin-Gay Sec. 13.1
Developmental Mathematics Third Edition, Elayn Martin-Gay Sec. 13.1 Section 13.1 The Greatest Common Factor and Factoring by Grouping Complete the outline as you view Lecture Video 13.1. Pause the video
More information8-7 Solving ax^2 + bx + c = 0
29. BASKETBALL When Jerald shoots a free throw, the ball is 6 feet from the floor and has an initial upward velocity of 20 feet per second. The hoop is 10 feet from the floor. a. Use the vertical motion
More informationFactors of 10 = = 2 5 Possible pairs of factors:
Factoring Trinomials Worksheet #1 1. b 2 + 8b + 7 Signs inside the two binomials are identical and positive. Factors of b 2 = b b Factors of 7 = 1 7 b 2 + 8b + 7 = (b + 1)(b + 7) 2. n 2 11n + 10 Signs
More informationUNIT 1 RELATIONSHIPS BETWEEN QUANTITIES AND EXPRESSIONS Lesson 1: Working with Radicals and Properties of Real Numbers
Guided Practice Example 1 Reduce the radical expression result rational or irrational? 80. If the result has a root in the denominator, rationalize it. Is the 1. Rewrite each number in the expression as
More informationAlgebra/Geometry Blend Unit #5: Factoring and Quadratic Functions Lesson 2: Factoring Trinomials. What does factoring really mean?
Algebra/Geometry Blend Unit #5: Factoring and Quadratic Functions Lesson 2: Factoring Trinomials Name Period Date [page 1] Before you embark on your next factoring adventure, it is important to ask yourself
More informationPolynomials * OpenStax
OpenStax-CNX module: m51246 1 Polynomials * OpenStax This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section students will: Abstract Identify
More information