Chapter 8 Class Notes 8-A1 (Lessons 8-1&8-2) Monomials and Factoring p Prime Factorization: a whole number expressed as the of factors.
|
|
- Abigail Cunningham
- 6 years ago
- Views:
Transcription
1 Chapter 8 Class Notes Alg. 1H 8-A1 (Lessons 8-1&8-) Monomials and Factoring p Prime Factorization: a whole number epressed as the of factors. Tree Method: Ladder Method: Factored Form of a Monomial: epressed as the product of and ; o no variable has an greater than. 1A) 38rs t 66 pq y Greatest Common Factor: : the of the factors; the greatest number that is a factor of original numbers. Relatively Prime: when or more integers or monomials have a GCF 3A) of 3 17 d ; 5d p q; 3 pr t 7 a b; 15ab c Ch. 8 Notes Alg. 1H 1
2 Factoring Using the Distributive Property p Factor a Polynomial: find its factored form. Use the ab ac a b c ab ac a b c 1A) 16a 4b p q pq pq D) 1y 4y 30 y 4 (p. 48) Zero Product Property: If the of factors is 0, then at least 1 of the factors must be equal to. Solve a Polynomial Equation: Read E Set the polynomial =.. completely 3. Determine the values of the variable that would make factor equal. (Solutions are also called.) 4A) 3nn 0 7d 35d 0 10 Ch. 8 Notes Alg. 1H
3 (p. 47) When a polynomial has 4 or more terms, factor by of terms. E.) y 7 4y 14 A) rs 5s r a ab a b Additive Inverses: Binomials that have opposite signs on each term. EX: 7 y and y 7 10 and 10 1 y 7 3A) c cd 8d 4 3p p 18p 7 Summary: Factor by Grouping 1. Use when there are or more terms.. Terms with can be grouped together. 3. The common binomial factors are or. 4. Algebraic Model: a b ay by a b y a b a b y or y a b Ch. 8 Notes Alg. 1H 3
4 8-A (Lesson 8-3) Factoring Trinomials: b c p When are multiplied, each binomial is a of the product. Factoring is like unwrapping the foil start with the and figure out what the factors are. Eamples: A. 3 C. 8 B A) a 8a t t A) 1 m m s 11s 8 3A) h 3h 40 r r 4 Ch. 8 Notes Alg. 1H 4
5 Solve Equations by Factoring: 1. Write the trinomial as an equal to.. completely. 3. Use the to find the solutions. 4. The solutions are also called. 4A) 16 8 g 6g 7 15 p. 437 #5 Check Your Progress p. 437 #7,9,11 Check Your Understanding Ch. 8 Notes Alg. 1H 5
6 8-A3 (Lesson 8-4) Factoring Trinomials: a b c p Guess and Check Method: possibilities. Check for correct term E. A) Practice will pay off! You will get better at this, and it will take less guesses before you find the correct factors! 1A) Always check for a BEFORE factoring a trinomial! 10y 35y 30 D) 6 8 Ch. 8 Notes Alg. 1H 6
7 Prime Polynomial: cannot be. A) 4r r Solve Equations by Factoring: 1. Write the trinomial as an equal to.. completely. 3. Use the to find the solutions. (The solutions are also called.) 3A) Ch. 8 Notes Alg. 1H 7
8 8-A4 (Lesson 8-4) Vertical Motion Model p. 444 h 16t vt s h = ending o in feet v = initial o speed and direction positive or negative o feet per second) s = height o in feet t = o in seconds o usually is the unknown value you have to figure out Model: Read E. 4 Pep Rally and do CYU #10 Cliff Diving Check Your Progress (under E. 4) Ch. 8 Notes Alg. 1H 8
9 8-A6 (Lesson 8-5) Factoring Differences of Squares p Difference of Squares: a b a b a b EX: or 3 3 1A) 81 t 64g h D) 3 4y 9 y Solve: E) 9t 49 0 F) Sometimes you have to apply the Difference of Squares Pattern more than to factor a polynomial. A) y 1 16a 16b 4 4 Use Several Factoring Techniques: 3A) r r r ) Solve: ) Ch. 8 Notes Alg. 1H 9
10 8-A7 (Lesson 8-6) Perfect Squares and Factoring p Review: Read p , Key Concepts and E. 1 and. Perfect Square Trinomial: a ab b a b a ab b a b E: The 1 st term must be a.. The middle term must be the product of the square roots of the and terms. 3. The last term must be a. 1A) n 4n D) y 8y 16 A) 3 9t 3t 0 p. 456 E. 3 Solving: 3A) a 1a y y D) 4y 36y 81 0 Ch. 8 Notes Alg. 1H 10
11 p. 457 Square Root Property: If n, then n E.: Use this property to solve the following equations: 4) h 16t h0 (The bridge is 100 ft. high.) A) z z 1 16 y 8 7 p. 455 Concept Summary: Factoring Polynomials # of Factoring Technique Terms or more 3 Difference of Squares Perfect Square Trinomial Leading coefficient is 1 Leading coefficient is not 1 Greatest Common Factor Eample 4 or more Grouping Ch. 8 Notes Alg. 1H 11
12 8-A8 Area and Vertical Motion Word Problems (Power Point) A. Geometry Problems: It helps to draw a sketch! 1. A triangle has an area of 40 cm. Find the height, h, of the triangle.. The length of a rectangular swimming pool is 0 ft. greater than its width. The area of the pool is 55 ft. What are its dimensions? 3. Four squares, each with side, are cut from a square piece of paper as shown. What value of will result in an area that is 7 of the 16 original area? B. Vertical Motion Problems: Learn the Formula! 4. While standing on the roof of a building that was 400 ft high, you dropped an egg. How many seconds will it take the egg to hit the ground? Ch. 8 Notes Alg. 1H 1
13 5. How long would it take a hammer to hit the roof of a truck if the hammer were dropped from a height of 70 ft? The roof of the truck is 6 ft high. 6. A rocket is launched from ground level at an initial velocity of 100 feet per second. How many seconds will it take for the rocket to return to the ground? 7. A football is kicked upward at a velocity of 4 ft per second (ft/s). When will it reach a height of 0 ft? 8. A soccer player kicks a soccer ball with a velocity of 3 ft/sec. If the ball reaches a height of 16 ft, how long does it stay in the air? Ch. 8 Notes Alg. 1H 13
Fair Game Review. Chapter 7. Simplify the expression. Write an expression for the perimeter of the figure
Name Date Chapter 7 Simplify the expression. Fair Game Review 1. 5y + 6 9y. h + 11 + 3h 4 + + 4. 7 ( m + 8) 3. 8a 10 4a 6 a 5. 5 ( d + 3) + 4( d 6) 6. q ( q ) 16 + 9 + 7 Write an expression for the perimeter
More informationUNIT 9 (Chapter 7 BI) Polynomials and Factoring Name:
UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay
More informationMaintaining Mathematical Proficiency
Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t 4 3. 8s 4 + 4s 6 5s 4. 9m + 3 + m 3 + 5m 5. 4 3p 7 3p 4 1 z 1 + 4 6. ( ) 7. 6( x + ) 4 8. 3( h + 4) 3( h
More informationChapter 3: Section 3.1: Factors & Multiples of Whole Numbers
Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Prime Factor: a prime number that is a factor of a number. The first 15 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
More informationThe number part of a term with a variable part. Terms that have the same variable parts. Constant terms are also like terms.
Algebra Notes Section 9.1: Add and Subtract Polynomials Objective(s): To be able to add and subtract polynomials. Recall: Coefficient (p. 97): Term of a polynomial (p. 97): Like Terms (p. 97): The number
More informationChapter 9 Notes Alg. 1H 9-A1 (Lesson 9-3) Solving Quadratic Equations by Finding the Square Root and Completing the Square
Chapter Notes Alg. H -A (Lesson -) Solving Quadratic Equations b Finding the Square Root and Completing the Square p. *Calculator Find the Square Root: take the square root of. E: Solve b finding square
More informationUnit 5 Quadratic Expressions and Equations
Unit 5 Quadratic Expressions and Equations Test Date: Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials and
More informationSecondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics
Secondary Math H Unit 3 Notes: Factoring and Solving Quadratics 3.1 Factoring out the Greatest Common Factor (GCF) Factoring: The reverse of multiplying. It means figuring out what you would multiply together
More information9-1 Skills Practice Factors and Greatest Common Factors Find the factors of each number. Then classify each number as prime or composite
9-1 Skills Practice Factors and Greatest Common Factors Find the factors of each number. Then classify each number as prime or composite. 1. 10 2. 31 3. 16 4. 52 5. 38 6. 105 Find the prime factorization
More informationUnit 5 AB Quadratic Expressions and Equations 1/9/2017 2/8/2017
Unit 5 AB Quadratic Expressions and Equations 1/9/2017 2/8/2017 Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials
More informationCollecting Like Terms
MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.
More informationAlgebra I Notes Unit Eleven: Polynomials
Syllabus Objective: 9.1 The student will add, subtract, multiply, and factor polynomials connecting the arithmetic and algebraic processes. Teacher Note: A nice way to illustrate operations with polynomials
More informationAlgebra 1B Final Review
Name: Class: Date: ID: A Algebra 1B Final Review Short Answer 1. Originally a rectangle was twice as long as it was wide. When 5 m was subtracted from its length and 3 m subtracted from its width, the
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 informationMathB65 Ch 4 IV, V, VI.notebook. October 31, 2017
Part 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest
More informationWhen factoring, we ALWAYS start with the (unless it s 1).
Math 100 Elementary Algebra Sec 5.1: The Greatest Common Factor and Factor By Grouping (FBG) Recall: In the product XY, X and Y are factors. Defn In an expression, any factor that is common to each term
More informationA-2. Polynomials and Factoring. Section A-2 1
A- Polynomials and Factoring Section A- 1 What you ll learn about Adding, Subtracting, and Multiplying Polynomials Special Products Factoring Polynomials Using Special Products Factoring Trinomials Factoring
More informationSection 9.1: Add and Subtract Polynomials. The number part of a term with a variable part.
Algebra Notes Section 9.1: Add and Subtract Polynomials Objective(s): Recall: Coefficient (p. 97): Term of a polynomial (p. 97): Like Terms (p. 97): The number part of a term with a variable part. The
More informationSection 1.7: Solving Equations by Factoring
Objective: Solve equations by factoring and using the zero product rule. When solving linear equations such as x 5 1, we can solve for the variable directly by adding 5 and dividing by to get 1. However,
More informationQuadratic Expressions and Equations
Unit 5 Quadratic Expressions and Equations 1/9/2017 2/8/2017 Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials
More information7.1 Practice A. w y represents the height of an object t seconds. Name Date
Name Date 7.1 Practice A In Eercises 1 3, find the degree of the monomial. 3 1. 7n. 1 w 5 3 3. 5 In Eercises 4 6, write the polnomial in standard form. Identif the degree and leading coefficient of the
More informationInstructor: Richard Getso Course: Math 200.P10 TR 1:00 PM Spring 2016 (Getso)
1/8/016 Practice Test 1 (Chapter 11) Richard Getso Student: Richard Getso Date: 1/8/16 Instructor: Richard Getso Course: Math 00.P10 TR 1:00 PM Spring 016 (Getso) Assignment: Practice Test 1 (Chapter 11)
More informationAlgebra I. Polynomials.
1 Algebra I Polynomials 2015 11 02 www.njctl.org 2 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying a Polynomial by a Monomial Multiplying
More informationDivisibility Rules Algebra 9.0
Name Period Divisibility Rules Algebra 9.0 A Prime Number is a whole number whose only factors are 1 and itself. To find all of the prime numbers between 1 and 100, complete the following eercise: 1. Cross
More informationSummer Prep Packet for students entering Algebra 2
Summer Prep Packet for students entering Algebra The following skills and concepts included in this packet are vital for your success in Algebra. The Mt. Hebron Math Department encourages all students
More informationMath 10-C Polynomials Concept Sheets
Math 10-C Polynomials Concept Sheets Concept 1: Polynomial Intro & Review A polynomial is a mathematical expression with one or more terms in which the exponents are whole numbers and the coefficients
More informationChapter 5: Exponents and Polynomials
Chapter 5: Exponents and Polynomials 5.1 Multiplication with Exponents and Scientific Notation 5.2 Division with Exponents 5.3 Operations with Monomials 5.4 Addition and Subtraction of Polynomials 5.5
More informationAlgebraic Expressions and Identities
9 Algebraic Epressions and Identities introduction In previous classes, you have studied the fundamental concepts of algebra, algebraic epressions and their addition and subtraction. In this chapter, we
More informationTEKS: 2A.10F. Terms. Functions Equations Inequalities Linear Domain Factor
POLYNOMIALS UNIT TEKS: A.10F Terms: Functions Equations Inequalities Linear Domain Factor Polynomials Monomial, Like Terms, binomials, leading coefficient, degree of polynomial, standard form, terms, Parent
More informationQuadratic Functions. Key Terms. Slide 1 / 200. Slide 2 / 200. Slide 3 / 200. Table of Contents
Slide 1 / 200 Quadratic Functions Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic Equations
More informationQuadratic Functions. Key Terms. Slide 2 / 200. Slide 1 / 200. Slide 3 / 200. Slide 4 / 200. Slide 6 / 200. Slide 5 / 200.
Slide 1 / 200 Quadratic Functions Slide 2 / 200 Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic
More informationSlide 1 / 200. Quadratic Functions
Slide 1 / 200 Quadratic Functions Key Terms Slide 2 / 200 Table of Contents Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic
More informationAlgebra I Unit Report Summary
Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02
More informationMini-Lecture 5.1 Exponents and Scientific Notation
Mini-Lecture.1 Eponents and Scientific Notation Learning Objectives: 1. Use the product rule for eponents.. Evaluate epressions raised to the zero power.. Use the quotient rule for eponents.. Evaluate
More informationTopic 7: Polynomials. Introduction to Polynomials. Table of Contents. Vocab. Degree of a Polynomial. Vocab. A. 11x 7 + 3x 3
Topic 7: Polynomials Table of Contents 1. Introduction to Polynomials. Adding & Subtracting Polynomials 3. Multiplying Polynomials 4. Special Products of Binomials 5. Factoring Polynomials 6. Factoring
More informationAlgebra I. Exponents and Polynomials. Name
Algebra I Exponents and Polynomials Name 1 2 UNIT SELF-TEST QUESTIONS The Unit Organizer #6 2 LAST UNIT /Experience NAME 4 BIGGER PICTURE DATE Operations with Numbers and Variables 1 CURRENT CURRENT UNIT
More information2 P a g e. Essential Questions:
NC Math 1 Unit 5 Quadratic Functions Main Concepts Study Guide & Vocabulary Classifying, Adding, & Subtracting Polynomials Multiplying Polynomials Factoring Polynomials Review of Multiplying and Factoring
More informationAlgebra Final Exam Review Packet
Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:
More informationAlgebra I Polynomials
Slide 1 / 217 Slide 2 / 217 Algebra I Polynomials 2014-04-24 www.njctl.org Slide 3 / 217 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying
More information7-7 Multiplying Polynomials
Example 1: Multiplying Monomials A. (6y 3 )(3y 5 ) (6y 3 )(3y 5 ) (6 3)(y 3 y 5 ) 18y 8 Group factors with like bases together. B. (3mn 2 ) (9m 2 n) Example 1C: Multiplying Monomials Group factors with
More informationName Class Date. Multiplying Two Binomials Using Algebra Tiles
Name Class Date Multiplying Polynomials Going Deeper Essential question: How do you multiply polynomials? 6-5 A monomial is a number, a variable, or the product of a number and one or more variables raised
More informationMathB65 Ch 4 VII, VIII, IX.notebook. November 06, 2017
Chapter 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest
More informationAlgebra 1: Hutschenreuter Chapter 10 Notes Adding and Subtracting Polynomials
Algebra 1: Hutschenreuter Chapter 10 Notes Name 10.1 Adding and Subtracting Polynomials Polynomial- an expression where terms are being either added and/or subtracted together Ex: 6x 4 + 3x 3 + 5x 2 +
More informationUNIT 2 FACTORING. M2 Ch 11 all
UNIT 2 FACTORING M2 Ch 11 all 2.1 Polynomials Objective I will be able to put polynomials in standard form and identify their degree and type. I will be able to add and subtract polynomials. Vocabulary
More informationPractice Mixed Exercises. Write each polynomial in standard form. Then name each polynomial by its degree and the number of its terms.
Practice 10-1 Write each polynomial in standard form. Then name each polynomial by its degree and the number of its terms. 1. 4y 3 4y 2 3 y 2. x 2 x 4 6 3. x 2 4. 2m 2 7m 3 3m 5. 4 x 2x 2 6. 7x 3 2x 2
More informationMultiplication of Polynomials
Summary 391 Chapter 5 SUMMARY Section 5.1 A polynomial in x is defined by a finite sum of terms of the form ax n, where a is a real number and n is a whole number. a is the coefficient of the term. n is
More informationFor Your Notebook E XAMPLE 1. Factor when b and c are positive KEY CONCEPT. CHECK (x 1 9)(x 1 2) 5 x 2 1 2x 1 9x Factoring x 2 1 bx 1 c
9.5 Factor x2 1 bx 1 c Before You factored out the greatest common monomial factor. Now You will factor trinomials of the form x 2 1 bx 1 c. Why So you can find the dimensions of figures, as in Ex. 61.
More information= The algebraic expression is 3x 2 x The algebraic expression is x 2 + x. 3. The algebraic expression is x 2 2x.
Chapter 7 Maintaining Mathematical Proficiency (p. 335) 1. 3x 7 x = 3x x 7 = (3 )x 7 = 5x 7. 4r 6 9r 1 = 4r 9r 6 1 = (4 9)r 6 1 = 5r 5 3. 5t 3 t 4 8t = 5t t 8t 3 4 = ( 5 1 8)t 3 4 = ()t ( 1) = t 1 4. 3(s
More informationLesson 3 Algebraic expression: - the result obtained by applying operations (+, -,, ) to a collection of numbers and/or variables o
Lesson 3 Algebraic expression: - the result obtained by applying operations (+, -,, ) to a collection of numbers and/or variables o o ( 1)(9) 3 ( 1) 3 9 1 Evaluate the second expression at the left, if
More informationACTIVITY: Classifying Polynomials Using Algebra Tiles
7. Polynomials classify polynomials? How can you use algebra tiles to model and ACTIVITY: Meaning of Prefixes Work with a partner. Think of a word that uses one of the prefixes with one of the base words.
More information9.3 Using the Quadratic Formula to Solve Equations
Name Class Date 9.3 Using the Quadratic Formula to Solve Equations Essential Question: What is the quadratic formula, and how can you use it to solve quadratic equations? Resource Locker Explore Deriving
More informationUnit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions
CP Algebra Unit -1: Factoring and Solving Quadratics NOTE PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor by grouping.
More informationMultiplying Monomials
320 Chapter 5 Polynomials Eample 1 Multiplying Monomials Multiply the monomials. a. 13 2 y 7 215 3 y2 b. 1 3 4 y 3 21 2 6 yz 8 2 a. 13 2 y 7 215 3 y2 13 521 2 3 21y 7 y2 15 5 y 8 Group coefficients and
More informationChapter 8 Polynomials and Factoring
Chapter 8 Polynomials and Factoring 8.1 Add and Subtract Polynomials Monomial A. EX: Degree of a monomial the of all of the of the EX: 4x 2 y Polynomial A or EX: Degree of a polynomial the of its terms
More informationLesson 10.1 Polynomials
Lesson 10.1 Polynomials Objectives Classify polynomials. Use algebra tiles to add polynomials. Add and subtract polynomials. A contractor is buying paint to cover the interior of two cubical storage tanks.
More informationCHAPTER 1 QUADRATIC FUNCTIONS AND FACTORING
CHAPTER 1 QUADRATIC FUNCTIONS AND FACTORING Big IDEAS: 1) Graphing and writing quadratic functions in several forms ) Solving quadratic equations using a variety of methods 3) Performing operations with
More informationReview for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition.
LESSON 6- Review for Mastery Integer Exponents Remember that means 8. The base is, the exponent is positive. Exponents can also be 0 or negative. Zero Exponents Negative Exponents Negative Exponents in
More informationSolving Quadratic Equations (Adapted from Core Plus Mathematics, Courses 1 and 2)
Solving Quadratic Equations (Adapted from Core Plus Mathematics, Courses 1 and ) In situations that involve quadratic functions, the interesting questions often require solving equations. For example,
More informationWhy It s Important. What You ll Learn
How could you solve this problem? Denali and Mahala weed the borders on the north and south sides of their rectangular yard. Denali starts first and has weeded m on the south side when Mahala says he should
More informationHow to write polynomials in standard form How to add, subtract, and multiply polynomials How to use special products to multiply polynomials
PRC Ch P_3.notebook How to write polynomials in standard form How to add, subtract, and multiply polynomials How to use special products to multiply polynomials How to remove common factors from polynomials
More information7-4. } The sum of the coefficients of the outer and inner products is b. Going Deeper Essential question: How can you factor ax 2 + bx + c?
Name Class Date 7-4 Factoring ax 2 + bx + c Going Deeper Essential question: How can you factor ax 2 + bx + c? You have learned how to factor a x 2 + bx + c when a = 1 by identifying the correct pair of
More information( ) Chapter 7 ( ) ( ) ( ) ( ) Exercise Set The greatest common factor is x + 3.
Chapter 7 Exercise Set 7.1 1. A prime number is an integer greater than 1 that has exactly two factors, itself and 1. 3. To factor an expression means to write the expression as the product of factors.
More information6-5 Multiplying Polynomials
6-5 Multiplying Polynomials Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Evaluate. 1.3 2 3.10 2 Simplify. 9 2.2 4 16 100 4.2 3 2 4 6. (5 3 ) 2 2 7 5. y 5 y 4 5 6 7.(x 2 ) 4 y 9 x 8 8. 4(x
More informationLecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 3rd edition. Miller, O'Neill, & Hyde. Victor Valley College
Lecture Guide Math 90 - Intermediate Algebra to accompany Intermediate Algebra, 3rd edition Miller, O'Neill, & Hyde Prepared by Stephen Toner Victor Valley College Last updated: 4/17/16 5.1 Exponents &
More information7.7. Factoring Special Products. Essential Question How can you recognize and factor special products?
7.7 Factoring Special Products Essential Question How can you recognize and factor special products? Factoring Special Products LOOKING FOR STRUCTURE To be proficient in math, you need to see complicated
More informationChapter 9 Resource Masters
Chapter 9 Resource Masters Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Study Guide
More informationIntermediate Algebra 100A Final Exam Review Fall 2007
1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,
More informationAdditional Factoring Examples:
Honors Algebra -3 Solving Quadratic Equations by Graphing and Factoring Learning Targets 1. I can solve quadratic equations by graphing. I can solve quadratic equations by factoring 3. I can write a quadratic
More informationUnit 3A: Factoring & Solving Quadratic Equations After completion of this unit, you will be able to
Unit 3A: Factoring & Solving Quadratic Equations After completion of this unit, you will be able to Learning Target #1: Factoring Factor the GCF out of a polynomial Factor a polynomial when a = 1 Factor
More informationACTIVITY: Factoring Special Products. Work with a partner. Six different algebra tiles are shown below.
7.9 Factoring Special Products special products? How can you recognize and factor 1 ACTIVITY: Factoring Special Products Work with a partner. Six different algebra tiles are shown below. 1 1 x x x 2 x
More information2. Write each number as a power of 10 using negative exponents.
Q Review 1. Simplify each expression. a. 1 0 b. 5 2 1 c. d. e. (7) 2 f. 6 1 g. 6 0 h. (12x) 2 i. 1 j. 6bc 0 0 8 k. (11x) 0 l. 2 2 9 m. m 8 p 0 n. 5a 2c k ( mn) o. p. 8 p 2m n q. 8 2 q r 5 r. (10a) b 0
More informationIntensive Math-Algebra I Mini-Lesson MA.912.A.4.3
Intensive Math-Algebra I Mini-Lesson M912.4.3 Summer 2013 Factoring Polynomials Student Packet Day 15 Name: Date: Benchmark M912.4.3 Factor polynomials expressions This benchmark will be assessed using
More informationx (vertex is halfway between the x-intercepts)
Big Idea: A quadratic equation in the form a b c 0 has a related function f ( ) a b c. The zeros of the function are the -intercepts of its graph. These -values are the solutions or roots of the related
More informationReview Notes - Solving Quadratic Equations
Review Notes - Solving Quadratic Equations What does solve mean? Methods for Solving Quadratic Equations: Solving by using Square Roots Solving by Factoring using the Zero Product Property Solving by Quadratic
More informationUnit 7: Factoring Quadratic Polynomials
Unit 7: Factoring Quadratic Polynomials A polynomial is represented by: where the coefficients are real numbers and the exponents are nonnegative integers. Side Note: Examples of real numbers: Examples
More informationMA 22000, Lesson 2 Functions & Addition/Subtraction Polynomials Algebra section of text: Sections 3.5 and 5.2, Calculus section of text: Section R.
MA 000, Lesson Functions & Addition/Subtraction Polynomials Algebra section of tet: Sections.5 and 5., Calculus section of tet: Section R.1 Definition: A relation is any set of ordered pairs. The set of
More informationAlgebra 2. Factoring Polynomials
Algebra 2 Factoring Polynomials Algebra 2 Bell Ringer Martin-Gay, Developmental Mathematics 2 Algebra 2 Bell Ringer Answer: A Martin-Gay, Developmental Mathematics 3 Daily Learning Target (DLT) Tuesday
More informationREVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES
Etra Eample. Graph.. 6. 7. (, ) (, ) REVIEW KEY VOCABULARY quadratic function, p. 6 standard form of a quadratic function, p. 6 parabola, p. 6 verte, p. 6 ais of smmetr, p. 6 minimum, maimum value, p.
More informationReady To Go On? Skills Intervention 7-1 Integer Exponents
7A Evaluating Expressions with Zero and Negative Exponents Zero Exponent: Any nonzero number raised to the zero power is. 4 0 Ready To Go On? Skills Intervention 7-1 Integer Exponents Negative Exponent:
More informationA monomial is measured by its degree To find its degree, we add up the exponents of all the variables of the monomial.
UNIT 6 POLYNOMIALS Polynomial (Definition) A monomial or a sum of monomials. A monomial is measured by its degree To find its degree, we add up the exponents of all the variables of the monomial. Ex. 2
More informationChapter 11: Factoring Polynomials Greatest Common Factor. ca d Factoring When Terms Have a Common Factor. Factor completely. B Å'B * # "& B Ä'B
Chapter 11: Factoring Polynomials Mr. Getso s Algebra Notes Spring 2015 11.1 Greatest Common Factor ca d Factoring When Terms Have a Common Factor 1. Factor completely. B Å'B * "& 2. B Ä B $ ( 3. B ÅB
More informationGet Ready. 6. Expand using the distributive property. a) 6m(2m 4) b) 8xy(2x y) c) 6a 2 ( 3a + 4ab) d) 2a(b 2 6ab + 7)
Get Ready BLM 5 1... Classify Polynomials 1. Classify each polynomial by the number of terms. 2y x 2 + 3x + 2 c) 6x 2 y + 2xy + 4 d) x 2 + y 2 e) 3x 2 + 2x + y 4 6. Expand using the distributive property.
More informationPrime Factorization and GCF. In my own words
Warm- up Problem What is a prime number? A PRIME number is an INTEGER greater than 1 with EXACTLY 2 positive factors, 1 and the number ITSELF. Examples of prime numbers: 2, 3, 5, 7 What is a composite
More informationCh. 9.3 Vertex to General Form. of a Parabola
Ch. 9.3 Verte to General Form Learning Intentions: of a Parabola Change a quadratic equation from verte to general form. Learn to square a binomial & factor perfectsquare epressions using rectangle diagrams.
More informationSolving Quadratic Equations
Solving Quadratic Equations MATH 101 College Algebra J. Robert Buchanan Department of Mathematics Summer 2012 Objectives In this lesson we will learn to: solve quadratic equations by factoring, solve quadratic
More informationQuadratic Functions and Equations
Quadratic Functions and Equations 9A Quadratic Functions 9-1 Quadratic Equations and Functions Lab Explore the Axis of Symmetry 9- Characteristics of Quadratic Functions 9-3 Graphing Quadratic Functions
More informationAlgebra 2/Trig Apps: Chapter 5 Quadratics Packet
Algebra /Trig Apps: Chapter 5 Quadratics Packet In this unit we will: Determine what the parameters a, h, and k do in the vertex form of a quadratic equation Determine the properties (vertex, axis of symmetry,
More informationPAP Algebra 2. Unit 4B. Quadratics (Part 2) Name Period
PAP Algebra Unit 4B Quadratics (Part ) Name Period 1 After Test WS: 4.6 Solve by Factoring PAP Algebra Name Factor. 1. x + 6x + 8. 4x 8x 3 + + 3. x + 7x + 5 4. x 3x 1 + + 5. x + 7x + 6 6. 3x + 10x + 3
More informationUnit 3 Factors & Products
1 Unit 3 Factors & Products General Outcome: Develop algebraic reasoning and number sense. Specific Outcomes: 3.1 Demonstrate an understanding of factors of whole number by determining the: o prime factors
More informationFactoring x 2 + bx + c
7.5 Factoring x 2 + bx + c Essential Question How can you use algebra tiles to factor the trinomial x 2 + bx + c into the product of two binomials? Finding Binomial Factors Work with a partner. Use algebra
More informationThe greatest common factor, or GCF, is the largest factor that two or more terms share.
Unit, Lesson Factoring Recall that a factor is one of two or more numbers or expressions that when multiplied produce a given product You can factor certain expressions by writing them as the product of
More information6-3 Polynomials. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1
6-3 Polynomials Warm Up Lesson Presentation Lesson Quiz Algebra 1 Objectives Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions. A polynomial is a monomial or
More informationUnit 3. Expressions and Equations. 118 Jordan School District
Unit 3 Epressions and Equations 118 Unit 3 Cluster 1 (A.SSE.): Interpret the Structure of Epressions Cluster 1: Interpret the structure of epressions 3.1. Recognize functions that are quadratic in nature
More informationAdditional Exercises 7.1 Form I The Greatest Common Factor and Factoring by Grouping
Additional Exercises 7.1 Form I The Greatest Common Factor and Factoring by Grouping Find the greatest common factor of each list of monomials. 1. 10x and 15 x 1.. 3 1y and 8y. 3. 16 a 3 a, 4 and 4 3a
More informationLESSON 7.2 FACTORING POLYNOMIALS II
LESSON 7.2 FACTORING POLYNOMIALS II LESSON 7.2 FACTORING POLYNOMIALS II 305 OVERVIEW Here s what you ll learn in this lesson: Trinomials I a. Factoring trinomials of the form x 2 + bx + c; x 2 + bxy +
More informationReview: Properties of Exponents (Allow students to come up with these on their own.) m n m n. a a a. n n n m. a a a. a b a
Algebra II Notes Unit Si: Polynomials Syllabus Objectives: 6. The student will simplify polynomial epressions. Review: Properties of Eponents (Allow students to come up with these on their own.) Let a
More informationLesson 2: Introduction to Variables
Lesson 2: Introduction to Variables Topics and Objectives: Evaluating Algebraic Expressions Some Vocabulary o Variable o Term o Coefficient o Constant o Factor Like Terms o Identifying Like Terms o Combining
More informationMATH98 Intermediate Algebra Practice Test Form A
MATH98 Intermediate Algebra Practice Test Form A MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y - 4) - (y + ) = 3y 1) A)
More informationTHE QUADRATIC QUANDARY
THE QUADRATIC QUANDARY By Jay Snyder jaysnydermathplus@comcast.net I II III IV V What is a Quadratic Equation? What is a Quadratic Used For? Solve the Quadratic by Factoring Quadratic Formula Application
More information