Selected Worked Homework Problems. Step 1: The GCF must be taken out first (if there is one) before factoring the hard trinomial.
|
|
|
- Todd Shaw
- 6 years ago
- Views:
Transcription
1 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 trinomial. There is no GCF so factor 2x 2 + 5x + 3 Create an Easy Trinomial by moving the coefficient of the x 2 term to the end of the trinomial and multiplying the constant term by that coefficient Move the 2 to the right end of the trinomial and multiply it by the constant 3 to get 6 2x 2 + 5x x 2 + 5x + 6 Step 3: Factor the easy trinomial ( x + 2) ( x + 3 ) Step 4: In step 1 you multiplied the constant 1 by the coefficient of the x 2 term. 2 x Now divide BOTH of the constants that have been added or subtracted form the x term in the factors by that the coefficient. reduce each fraction that can be reduced (no mixed numbers) 2 x + 2 ( ) ( 2x + 3) ( x +1) You can check your answer by FOIL ing the factors ( 2x + 3) ( x +1) = 2x 2 + x + 4x + 3 = 2x 2 + 5x + 3 Math 100 Section 7 4 HW WKD 2016 Eitel
2 2. 3x 2 2x 5 Step 1. There is no GCF so factor 3x 2 2x 5 3x 2 2x 5 3 x 2 2x 15 Step 3: Factor the easy trinomial ( x 5 ) ( x + 3 ) Step 4: Divide each constant added or subtracted from x by 3 x and then reduce each fraction that can be reduced (no mixed numbers) x 5 3 ( x +1) Answer: ( 3x 5) ( x +1) You can check your answer by FOIL ing the factors ( 3x 5) ( 2x + 3) = 6x 2 + 9x 10x 15 = 6x 2 x 15 Math 100 Section 7 4 HW WKD 2016 Eitel
3 3. 6x 2 + 7x 3 Step 1. There is no GCF so factor 6x 2 + 7x 3 6x 2 + 7x 3 6 x 2 + 7x 18 Step 3: Factor the easy trinomial ( x 2 ) ( x + 9 ) Step 4: Divide each constant added or subtracted from x by 6 x 2 x and then reduce each fraction that can be reduced (no mixed numbers) x Answer: ( 3x 1) ( 2x + 3) You can check your answer by FOIL ing the factors ( 3x 1) ( 2x + 3) = 6x 2 + 7x 2x + 3 = 6x 2 + 7x + 3 Math 100 Section 7 4 HW WKD 2016 Eitel
4 4. 4x 2 5x 6 Step 1. There is no GCF so factor 4x 2 5x 6 4x 2 5x 6 4 x 2 5x 24 Step 3: Factor the easy trinomial ( x + 3 ) ( x 8 ) Step 4: Divide each constant added or subtracted from x by 4 4 x 8 4 and then reduce each fraction that can be reduced (no mixed numbers) 4 x 2 ( ) Answer: ( 4x + 3) ( x 2) You can check your answer by FOIL ing the factors ( 4x + 3) ( x 2) = 4x 2 + 3x 8x 6 = 4x 2 5x + 6 Math 100 Section 7 4 HW WKD 2016 Eitel
5 5. 8x 2 17x + 2 Step 1. There is no GCF so factor 8x 2 17x + 2 8x 2 17x x 2 17x +16 Step 3: Factor the easy trinomial ( x - 1) ( x 16 ) Step 4: Divide each constant added or subtracted from x by 8 x 1 8 x 16 8 and then reduce each fraction that can be reduced (no mixed numbers) x 1 8 x 2 ( ) Answer: ( 8x 1) ( x 2) You can check your answer by FOIL ing the factors ( 8x 1) ( x 2) = 16x 2 1x 16x + 2 = 8x 2 16x + 2 Math 100 Section 7 4 HW WKD 2016 Eitel
6 6. 3x 2 + 7x + 8 Step 1. There is no GCF so factor 3x 2 + 7x + 8 3x 2 + 7x x 2 + 7x + 24 Step 3: Factor the easy trinomial x 2 + 7x + 24 DOES NOT FACTOR so 3x 2 + 7x + 8 DOES NOT FACTOR 14. 9x 2 + 6x +1 Step 1. There is no GCF so factor 9x 2 + 6x +1 9x 2 + 6x +1 9 x 2 + 6x + 9 Step 3: Factor the easy trinomial ( x + 3) ( x + 3) Step 4: Divide each constant added or subtracted from x by and then reduce each fraction that can be reduced (no mixed numbers) x + 1 x Answer: ( 3x +1) ( 3x +1) Math 100 Section 7 4 HW WKD 2016 Eitel
7 15. 5x 2 7x +1 Step 1. There is no GCF so factor 5x 2 7x +1 5x 2 7x +1 5 x 2 7x + 5 Step 3: Factor the easy trinomial x 2 7x + 5 DOES NOT FACTOR so 5x 2 7x +1 DOES NOT FACTOR x 2 + 5x 3 Step 1. There is no GCF so factor 12x 2 + 5x 3 12x 2 + 5x 3 12 x 2 + 5x 36 Step 3: Factor the easy trinomial ( x 4) ( x + 9) Step 4: Divide each constant added or subtracted from x by 12 x 4 12 x and then reduce each fraction that can be reduced (no mixed numbers) x Answer: ( 3x 1) ( 4x + 3) Math 100 Section 7 4 HW WKD 2016 Eitel
8 Factoring Completely: Step 1: Factor out the GCF Factor the expression inside the parenthesis x 2 +10x + 6 Step 1. The GCF is 2. Factor out a 2 4x 2 +10x + 6= 2 ( 2x 2 + 5x + 3) now factor 2x 2 + 5x + 3 2x 2 + 5x x 2 + 5x + 6 Step 3: Factor the easy trinomial 2 ( x +3 ) ( x + 2 ) Step 4: Divide each constant added or subtracted from x by x and then reduce each fraction that can be reduced (no mixed numbers) 2 x x +1 ( ) Answer: 2 ( 2x + 3) ( x +1) Math 100 Section 7 4 HW WKD 2016 Eitel
9 Factoring Completely: Step 1: Factor out the GCF Factor the expression inside the parenthesis x 2 +10x 4 Step 1. The GCF is 2. Factor out a 2 6x 2 +10x 4 = 2 ( 3x 2 + 5x 2) now factor 3x 2 + 5x 2 3x 2 + 5x 2 3 x 2 + 5x 6 Step 3: Factor the easy trinomial 2 ( x 1 ) ( x + 6 ) Step 4: Divide each constant added or subtracted from x by 3 2 x 1 3 x and then reduce each fraction that can be reduced (no mixed numbers) 2 x 1 3 x + 2 ( ) Answer: 2 ( 3x 1) ( x + 2) Math 100 Section 7 4 HW WKD 2016 Eitel
10 Factor Completely x 2 30x + 9 Step 1. The GCF is 3. Factor out a 3 6x 2 30x + 9 = 3( 2x 2 10x + 3) now factor 2x 2 10x + 3 2x 2 10x x 2 10x + 6 Step 3: Factor the easy trinomial x 2 10x + 6 DOES NOT FACTOR so Answer: 3( 2x 2 10x + 3) Note: DNF is not correct. You factored out a 3 so the original polynomial DID factor ( ) does not factor any further, but 3 2x 2 10x + 3 Math 100 Section 7 4 HW WKD 2016 Eitel
Factoring Trinomials of the Form
Section 7 3: Factoring Trinomials of the Form 1x 2 + Bx + C The FOIL process changes a product of 2 binomials into a polynomial. The reverse process starts with a polynomial and finds the 2 binomials whose
Tool 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
8-4 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.
University 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
2 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)
Factor 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
Algebra 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
Chapter 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,
Polynomial 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.
Lesson 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
Section 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
Chapter 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
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. 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
POD. 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
We 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
Unit 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
Review Journal 6 Assigned Work: See Website
MFM2P Polynomial Checklist 1 Goals for this unit: I can apply the distributive law to the product of binomials. I can complete the following types of factoring; common, difference of squares and simple
Name Class Date. There are several important things you should remember from multiplying binomials.
Name Class Date 7-3 Factoring x 2 + bx + c Going Deeper Essential question: How can you factor x 2 + bx + c? 1 A-SSE.1.2 ENGAGE Factoring Trinomials You know how to multiply binomials: for example, (x
Unit 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
-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
Identifying & 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
Accuplacer 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
Algebra. 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
UNIT 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
D This process could be written backwards and still be a true equation. = A D + B D C D
Section 4 2: Dividing Polynomials Dividing Polynomials if the denominator is a monomial. We add and subtract fractions with a common denominator using the following rule. If there is a common denominator
7.1 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
Algebra/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
Factoring Methods. Example 1: 2x * 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
Unit: Polynomials and Factoring
Unit: Polynomials: Multiplying and Factoring Name Dates Taught Specific Outcome 10I.A.1 Demonstrate an understanding of factors of whole numbers by determining: Prime factors Greatest common factor Least
Factoring 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
Is 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
a*(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
Name: 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
Math 154 :: Elementary Algebra
Math 1 :: Elementar Algebra Section.1 Exponents Section. Negative Exponents Section. Polnomials Section. Addition and Subtraction of Polnomials Section. Multiplication of Polnomials Section. Division of
Chapter 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
Section 8 2: Multiplying or Dividing Rational Expressions
Section 8 2: Multiplying or Dividing Rational Expressions Multiplying Fractions The basic rule for multiplying fractions is to multiply the numerators together and multiply the denominators together a
Unit 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
Section 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
Slide 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
P.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
Alg2A Factoring and Equations Review Packet
1 Multiplying binomials: We have a special way of remembering how to multiply binomials called FOIL: F: first x x = x 2 (x + 7)(x + 5) O: outer x 5 = 5x I: inner 7 x = 7x x 2 + 5x +7x + 35 (then simplify)
(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
Simplifying and Combining Like Terms Exponent
Simplifying and Combining Like Terms Exponent Coefficient 4x 2 Variable (or Base) * Write the coefficients, variables, and exponents of: a) 8c 2 b) 9x c) y 8 d) 12a 2 b 3 Like Terms: Terms that have identical
Factoring 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,
Week 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
1/14/15. Objectives. 7-5 Factoring Special Products. Factor perfect-square trinomials. Factor the difference of two squares.
Objectives Factor perfect-square trinomials. Factor the difference A trinomial is a perfect square if: The first and last terms are perfect squares. The middle term is two times one factor from the first
Section 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
TERMINOLOGY 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
Alg2A 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
Factoring 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 +
Multiplication of Polynomials
Multiplication of Polynomials In multiplying polynomials, we need to consider the following cases: Case 1: Monomial times Polynomial In this case, you can use the distributive property and laws of exponents
Factoring 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
Skills 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
7-4 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
Section 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:
Chapter 2 Algebra Part 1
Chapter 2 Algebra Part 1 Section 2.1 Expansion (Revision) In Mathematics EXPANSION really means MULTIPLY. For example 3(2x + 4) can be expanded by multiplying them out. Remember: There is an invisible
Math 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
Developmental 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
Step one is identifying the GCF, and step two is dividing it out.
Throughout this course we will be looking at how to undo different operations in algebra. When covering exponents we showed how ( 3) 3 = 27, then when covering radicals we saw how to get back to the original
How 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:
2-4 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.
6-3 Dividing Polynomials
Polynomials can be divided using long division just like you learned with numbers. Divide) 24 6 5 6 24-8 4-0 4 Remainder 24 6 = 5 4 6 Example : Using Long Division to Divide a Polynomial Divide using
FACTORING 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
The two meanings of Factor
Name Lesson #3 Date: Factoring Polynomials Using Common Factors Common Core Algebra 1 Factoring expressions is one of the gateway skills necessary for much of what we do in algebra for the rest of the
The two meanings of Factor 1. Factor (verb) : To rewrite an algebraic expression as an equivalent product
At the end of Packet #1we worked on multiplying monomials, binomials, and trinomials. What we have to learn now is how to go backwards and do what is called factoring. The two meanings of Factor 1. Factor
CCAC 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
Lesson 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
Name 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
ACCUPLACER 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
MATH 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.
2.01 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
In this section we revisit two special product forms that we learned in Chapter 5, the first of which was squaring a binomial.
5B. SPECIAL PRODUCTS 11 5b Special Products Special Forms In this section we revisit two special product forms that we learned in Chapter 5, the first of which was squaring a binomial. Squaring a binomial.
Topic 12 Factorisation
Topic 12 Factorisation 1. How to find the greatest common factors of an algebraic expression. Definition: A factor of a number is an integer that divides the number exactly. So for example, the factors
Downloaded 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
Name 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:
MTH 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),
Completing the Square. A trinomial that is the square of a binomial. x Squaring 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
Prerequisites. 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
Unit 9 Notes: Polynomials and Factoring. Unit 9 Calendar: Polynomials and Factoring. Day Date Assignment (Due the next class meeting) Monday Wednesday
Name Period Unit 9 Calendar: Polynomials and Factoring Day Date Assignment (Due the next class meeting) Monday Wednesday 2/26/18 (A) 2/28/18 (B) 9.1 Worksheet Adding, Subtracting Polynomials, Multiplying
Name 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
Factor Trinomials of the Form ax^2+bx+c
OpenStax-CNX module: m6018 1 Factor Trinomials of the Form ax^+bx+c Openstax Elementary Algebra This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 By
6.3 Factor Special Products *
OpenStax-CNX module: m6450 1 6.3 Factor Special Products * Ramon Emilio Fernandez Based on Factor Special Products by OpenStax This work is produced by OpenStax-CNX and licensed under the Creative Commons
The Zero Product Law. Standards:
Objective: Students will be able to (SWBAT) use complex numbers in polynomial identities and equations, in order to (IOT) solve quadratic equations with real coefficient that have complex solutions. Standards:
Mini-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
Math 10 Lesson 2-3 Factoring trinomials
I. Lesson Objectives: Math 10 Lesson 2-3 Factoring trinomials a) To see the patterns in multiplying binomials that can be used to factor trinomials into binomials. b) To factor trinomials of the form ax
3.1 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
Factoring 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
Multiply 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
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
Getting 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.
7-5 Factoring Special Products
7-5 Factoring Special Products Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Determine whether the following are perfect squares. If so, find the square root. 1. 64 yes; 8 2. 36 3. 45 no 4.
5.1 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
In the previous section, we added and subtracted polynomials by combining like terms. In this section, we extend that idea to radicals.
4.2: Operations on Radicals and Rational Exponents In this section, we will move from operations on polynomials to operations on radical expressions, including adding, subtracting, multiplying and dividing
We 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
Section 1.5: Factoring Special Products
Objective: Identify and factor special products including a difference of two perfect squares, perfect square trinomials, and sum and difference of two perfect cubes. When factoring there are a few special
Section 5.3 Factor By Grouping
Section 5.3 Factor By Grouping INTRODUCTION In the previous section you were introduced to factoring out a common monomial factor from a polynomial. For example, in the binomial 6x 2 + 15x, we can recognize
Name. 5. Simplify. a) (6x)(2x 2 ) b) (5pq 2 )( 4p 2 q 2 ) c) (3ab)( 2ab 2 )(2a 3 ) d) ( 6x 2 yz)( 5y 3 z)
3.1 Polynomials MATHPOWER TM 10, Ontario Edition, pp. 128 133 To add polynomials, collect like terms. To subtract a polynomial, add its opposite. To multiply monomials, multiply the numerical coefficients.
Algebra 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
Chapter 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
9/16/ (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