# Algebra Ch. 9.2 Multiplying Polynomials. Mr. Deyo

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Algebra Ch. 9.2 Multiplying Polynomials Mr. Deyo

2 Learning Target By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication. I will demonstrate this by completing Four(4) Square notes and by solving problems in a pair/group activity.

3 Home Work 1 2 3: 1) Class 4 Square Notes Put In Binder? 2) Section 9.2 TxtBk. Pg 531 Problems 7, 13, 15, 17 29, 35, 41, 43 Solved and Put in Binder? 3) Section Notes Copied on a blank sheet of paper in Binder? Table of Contents Date Description Date Due

4 Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1.How are the two images similar? 2.How are they different? 3.How can these two images be related to math?

5 Vocabulary 1) FOIL (First, Outer + Inner, Last) 2) Polynomial 3) Binomial 4) Trinomial

6 Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example Word List Friendly Definition Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing

7 Daily Warm-Up ExercisesFor For use use with with pages pages xxx xxx Simplify 2 (9a b) 2. Simplify r 2 s rs 3 3) Find the product 3x ( ) 2x 3

8 Daily Warm-Up ExercisesFor For use use with with pages pages xxx xxx Simplify 2 (9a b) ANSWER 18a + 2b 2. Simplify r 2 s rs 3 ANSWER r 3 s 4 3) Find the product 3x ( 2x 3 ). 3x ( 2x 3 ) =3 ( 2 ) x x 3 Regroup factors. = 6x 4 Simplify.

9 Notes: 3 Methods of Multiplying Polynomials: *1) # by # Table 2) FOIL (x + 2) (x + 2) (a + b) (c + d) 3) Vertical Multiplication x 2 + 4x + 4 ac + ad + bc + bd * Preferred Method

10 Example 3 Multiply polynomials using a table Problem A Find the product ( x 4( ) 3x +2).

11 Example 3 Multiply polynomials using a table Problem A Find the product ( x 4( ) 3x +2). SOLUTION STEP 1 Write subtraction as addition: ( x 4( ) 3x +2 ) = [ x +( 4) ]( 3x +2) STEP 2 Make a table of products. 3x 2 3x 2 x 3x 2 x 3x 2 2x x 8 ANSWER The product is 3x 2 + 2x 12x 8, or 3x 2 10x 8.

12 Guided Practice Problems B Find the product. 1. 5x 3 ( 3x) 2. x ( 7x 2 +4) 3. ( 4n 1( ) n +5)

13 Guided Practice Problems B Find the product. 1. 5x 3 ( 3x) ANSWER 15x 4 2. x ( 7x 2 +4) ANSWER 7x 3 +4x 3. ( 4n 1( ) n +5) ANSWER 4n 2 +19n 5

14 Storm Check (Think, Write, Discuss, Report) If multiplying polynomials, how would you modify the table for a binomial by a trinomial (2 x 3) or a trinomial by a trinomial (3 x 3)? For a binomial multiplied by a trinomial (2 x 3), I. For a trinomial multiplied by a trinomial (3 x 3), I.

15 Learning Target By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication. I will demonstrate this by completing Four(4) Square notes and by solving problems in a pair/group activity.

16 Home Work 1 2 3: 1) Class 4 Square Notes Put In Binder? 2) Section 3) Section TxtBk. Problems Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

17 Example 4 Find the product +b 2 Multiply polynomials vertically or by using a table (Problem A) +3b -4 ( b 2 +6b 7) ( 3b 4). +6b -7

18 Example 4 Find the product Multiply polynomials vertically or by using a table (Problem A Check) +3b -4 ( b 2 +6b 7) ( 3b 4). +b 2 +6b 3b 3 4b 2 +18b 2 24b -7 21b +28 3b b 2 45b+28

19 Example 4 Multiply polynomials vertically Find the product ( b 2 +6b 7) ( 3b 4). SOLUTION STEP 1 Multiply by 4. b 2 +6b 7 STEP 2 Multiply by 3b. b 2 +6b 7 3b 4 3b 4 4b 2 24b +28 4b 2 24b +28 3b b 2 21b

20 Example 4 Multiply polynomials vertically STEP 3 Add products. b 2 +6b 7 3b 4 4b 2 24b +28 3b b 2 21b 3b b 2 45b +28

21 Example 5 Multiply polynomials Problem B Find the product ( 2x 2 +5x 1( ) 4x 3). +4x -3 +2x 2 +6x -1

22 Example 5 Multiply polynomials Problem B Find the product ( 2x 2 +5x 1( ) 4x 3). +4x -3 +2x 2 +8x 3 6x 2 +6x +24x 2 18x -1 4x +3 = 8x 3 +14x 2 19x +3

23 Example 6 Multiply binomials using the FOIL pattern Find the product ( 3a +4) ( a 2). ( 3a +4) ( a 2) = ( 3a )( a ) + ( 3a )( 2) + ( 4) ( a ) + ( 4) ( 2) =3a 2 + ( 6a) + 4a + ( 8) =3a 2 2a 8 Write products of terms. Multiply. Combine like terms.

24 Guided Practice for Examples 4, 5, and 6 Find the product. 4. ( x 2 +2x +1( ) x +2) ANSWER x 3 +4x 2 +5x ( 3y 2 y +5 )( 2y 3) ANSWER 6y 3 11y 2 +13y ( 4b 5( ) b 2) ANSWER 4b 2 13b +10

25 Guided Practice for Examples 4, 5, and 6 Find the product. 4. ( x 2 +2x +1( ) x +2) 6. ( 4b 5( ) b 2) 5. ( 3y 2 y +5 )( 2y 3)

26 Storm Check (Think, Write, Discuss, Report) Of the three methods to multiply polynomials, which do you prefer to use? Why? I prefer to use the method because.

27 Learning Target By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication. I will demonstrate this by completing Four(4) Square notes and by solving problems in a pair/group activity.

28 Home Work 1 2 3: 1) Class 4 Square Notes Put In Binder? 2) Section 3) Section TxtBk. Problems Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

29 Vocabulary Review 1) FOIL (First, Outer + Inner, Last) 2) Polynomial 3) Binomial 4) Trinomial

30 Example 7 Solve a multi-step problem SKATEBOARDING You are designing a rectangular skateboard park on a lot that is on the corner of a city block. The park will be bordered by a walkway along two sides. The dimensions of the lot and the walkway are shown in the diagram. Write a polynomial that represents the area of the skateboard park.

31 Example 7 Solve a multi-step problem SOLUTION a. Write a polynomial using the formula for the area of a rectangle. The park s length is the lot s length minus the width of the sidewalk, or 45 x. Similarly, the park s width is 33 x.

32 Example 7 Solve a multi-step problem Area = length width Formula for area of a rectangle =( 45 x )( 33 x) Substitute for length and width. = x 33x + x 2 Multiply binomials. = x + x 2 Combine like terms. b. What is the area of the park if the walkway is 3 feet wide? (45-3) (33-3) (42)(30) 1260 square feet

### MS Algebra Ch Simplifying Rational Expressions. Mr. Deyo

MS Algebra Ch. 11.2 Simplifying Rational Expressions Mr. Deyo Title: 11.2 Simplifying Rational Expressions Date: Learning Target By the end of the period, I will simplify rational expressions and determine

### MS Algebra Ch. 7.6 Uniform Motion Problems. Mr. Deyo

MS Algebra Ch. 7.6 Uniform Motion Problems Mr. Deyo Title: Uniform Motion Date: Learning Target By the end of the period, I will apply the concept of uniform motion to solve for the desired variable in

### MS Algebra A-CED-1 Ch. 1.4 Write Equations & Inequalities

MS Algebra A-CED-1 Ch. 1.4 Write Equations & Inequalities ALGEBRA SUPPORT Write verbal phrases as algebraic equations or inequalities using appropriate terms, factors, and coefficients Title: 1.4 Write

### Maintaining 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

### Maintaining 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

### Activity 1 Multiply Binomials. Activity 2 Multiply Binomials. You can use algebra tiles to find the product of two binomials.

Algebra Lab Multiplying Polynomials You can use algebra tiles to find the product of two binomials. Virginia SOL A..b The student will perform operations on polynomials, including adding, subtracting,

### Factoring 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

### 7-7 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

### Degree of a polynomial

Variable Algebra Term Polynomial Monomial Binomial Trinomial Degree of a term Degree of a polynomial Linear A generalization of arithmetic. Letters called variables are used to denote numbers, which are

### Pre-Algebra 2. Unit 9. Polynomials Name Period

Pre-Algebra Unit 9 Polynomials Name Period 9.1A Add, Subtract, and Multiplying Polynomials (non-complex) Explain Add the following polynomials: 1) ( ) ( ) ) ( ) ( ) Subtract the following polynomials:

### Name Period Date. Use mathematical reasoning to create polynomial expressions that generalize patterns. Practice polynomial arithmetic.

Name Period Date POLYNOMIALS Student Packet 4: Polynomial Arithmetic Applications POLY4.1 Hundred Chart Patterns Gather empirical data to form conjectures about number patterns. Write algebraic expressions.

### Multiplying Polynomials. The rectangle shown at the right has a width of (x + 2) and a height of (2x + 1).

Page 1 of 6 10.2 Multiplying Polynomials What you should learn GOAL 1 Multiply two polynomials. GOAL 2 Use polynomial multiplication in real-life situations, such as calculating the area of a window in

### Dividing Polynomials

3-3 3-3 Dividing Polynomials Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Divide using long division. 1. 161 7 2. 12.18 2.1 23 5.8 Divide. 3. 4. 6x + 15y 3 7a 2 ab a 2x + 5y 7a b Objective

### Lesson 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

### Math 2 Variable Manipulation Part 3 Polynomials A

Math 2 Variable Manipulation Part 3 Polynomials A 1 MATH 1 REVIEW: VOCABULARY Constant: A term that does not have a variable is called a constant. Example: the number 5 is a constant because it does not

### 2 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

### Multiplying 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

### 21.1 Solving Equations by Factoring

Name Class Date 1.1 Solving Equations by Factoring x + bx + c Essential Question: How can you use factoring to solve quadratic equations in standard form for which a = 1? Resource Locker Explore 1 Using

### Understand the vocabulary used to describe polynomials Add polynomials Subtract polynomials Graph equations defined by polynomials of degree 2

Section 5.1: ADDING AND SUBTRACTING POLYNOMIALS When you are done with your homework you should be able to Understand the vocabulary used to describe polynomials Add polynomials Subtract polynomials Graph

### Factors of Polynomials Factoring For Experts

Factors of Polynomials SUGGESTED LEARNING STRATEGIES: Shared Reading, Activating Prior Knowledge, Discussion Group, Note-taking When you factor a polynomial, you rewrite the original polynomial as a product

### Algebra 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

### For 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.

### Polynomials Practice Test

Name: Class: Date: Polynomials Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. From the list, which terms are like 7x? 7x 2, 6x, 5, 8x, 7x,

### Chapter 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

### Name: Chapter 7: Exponents and Polynomials

Name: Chapter 7: Exponents and Polynomials 7-1: Integer Exponents Objectives: Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. You

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

### Name 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

### Unit 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

### Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together.

UNIT 10 Working with Polynomials The railcars are linked together. 370 UNIT 10 WORKING WITH POLYNOMIALS Just as a train is built from linking railcars together, a polynomial is built by bringing terms

### 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.

Chapter 8 Class Notes Alg. 1H 8-A1 (Lessons 8-1&8-) Monomials and Factoring p. 40-4 Prime Factorization: a whole number epressed as the of factors. Tree Method: Ladder Method: Factored Form of a Monomial:

### Chapter 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

### Section 1.1. Chapter 1. Quadratics. Parabolas. Example. Example. ( ) = ax 2 + bx + c -2-1

Chapter 1 Quadratic Functions and Factoring Section 1.1 Graph Quadratic Functions in Standard Form Quadratics The polynomial form of a quadratic function is: f x The graph of a quadratic function is a

### Algebra 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

### Math "Adding and Subtracting Polynomials" Bibiana Lopez. July Riverside City College. (RCC) 10.1 July / 15

Math 64 10.1 "Adding and Subtracting Polynomials" Bibiana Lopez Riverside City College July 2010 (RCC) 10.1 July 2010 1 / 15 Objectives: * Add and subtract polynomials. * Evaluate polynomials at given

### When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut.

Squaring a Binomial When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut. Solve. (x 3) 2 Step 1 Square the first term. Rules

### Sections 7.2, 7.3, 4.1

Sections 7., 7.3, 4.1 Section 7. Multiplying, Dividing and Simplifying Radicals This section will discuss the rules for multiplying, dividing and simplifying radicals. Product Rule for multiplying radicals

### Monomial. 5 1 x A sum is not a monomial. 2 A monomial cannot have a. x 21. degree. 2x 3 1 x 2 2 5x Rewrite a polynomial

9.1 Add and Subtract Polynomials Before You added and subtracted integers. Now You will add and subtract polynomials. Why? So you can model trends in recreation, as in Ex. 37. Key Vocabulary monomial degree

### To Find the Product of Monomials. ax m bx n abx m n. Let s look at an example in which we multiply two monomials. (3x 2 y)(2x 3 y 5 )

5.4 E x a m p l e 1 362SECTION 5.4 OBJECTIVES 1. Find the product of a monomial and a polynomial 2. Find the product of two polynomials 3. Square a polynomial 4. Find the product of two binomials that

### Grades ALGEBRA TILES. Don Balka and Laurie Boswell. Rowley, MA didax.com

Grades 6 12 ALGEBRA TILES Don Balka and Laurie Boswell Rowley, MA 01969 didax.com CONTENTS Introduction Correlation to the h Standards Unit 1: Introduction to Algebra Tiles 1 Overview and Answers 2 Activity

### MATHEMATICS 9 CHAPTER 7 MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT NAME: DATE: BLOCK: TEACHER: Miller High School Mathematics Page 1

MATHEMATICS 9 CHAPTER 7 NAME: DATE: BLOCK: TEACHER: MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT Miller High School Mathematics Page 1 Day 1: Creating expressions with algebra tiles 1. Determine the multiplication

### Westside Algebra 2 PreAP

Westside Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for

### Unit 3: Review for Final Exam

Unit 3: Review for Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the prime factorization of 1386. a. b. c. d. 2. Determine the greatest

### Summer 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

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

### Algebra 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 +

### Algebraic Expressions

Algebraic Expressions 1. Expressions are formed from variables and constants. 2. Terms are added to form expressions. Terms themselves are formed as product of factors. 3. Expressions that contain exactly

### MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline

MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline 1. Real Numbers (33 topics) 1.3 Fractions (pg. 27: 1-75 odd) A. Simplify fractions. B. Change mixed numbers

### Polynomials and Polynomial Equations

Polynomials and Polynomial Equations A Polynomial is any expression that has constants, variables and exponents, and can be combined using addition, subtraction, multiplication and division, but: no division

### Polynomials. This booklet belongs to: Period

HW Mark: 10 9 8 7 6 RE-Submit Polynomials This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. REVIEW TEST Your teacher

### A 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

### UNIT 8: LINEAR FUNCTIONS WEEK 31: Student Packet

Name Period Date UNIT 8: LINEAR FUNCTIONS WEEK 31: Student Packet 31.1 Introduction to Systems of Equations Use variables to write equations and systems of equations. Solve problems involving rate, distance,

### Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10. Unit 8. [Polynomials] Unit 8 Polynomials 1

Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 8 [Polynomials] Unit 8 Polynomials 1 To be a Successful Algebra class, TIGERs will show #TENACITY during

### POLYNOMIAL: A polynomial is a or the

MONOMIALS: CC Math I Standards: Unit 6 POLYNOMIALS: INTRODUCTION EXAMPLES: A number 4 y a 1 x y A variable NON-EXAMPLES: Variable as an exponent A sum x x 3 The product of variables 5a The product of numbers

### Two-Digit Number Times Two-Digit Number

Lesson Two-Digit Number Times Two-Digit Number Common Core State Standards 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using

### Combining Like Terms in Polynomials

Section 1 6: Combining Like Terms in Polynomials Polynomials A polynomial is an expression that has two or more terms each separated by a + or sign. If the expression has only one term it is called a monomial.

### Vocabulary Polynomial: A monomial or the sum of two or more monomials whose exponents are positive. Example: 5a 2 + ba 3. 4a b, 1.

A.APR.A.1: Arithmetic Operations on Polynomials POLYNOMIALS AND QUADRATICS A.APR.A.1: Arithmetic Operations on Polynomials A. Perform arithmetic operations on polynomials. 1. Understand that polynomials

### 1 of 32 4/24/2018, 11:38 AM

1 of 3 4/4/018, 11:38 AM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework149aleks 1 Insert < or > between the pair of integers to make the statement

### ACTIVITY: 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

### Topics Covered in Math 115

Topics Covered in Math 115 Basic Concepts Integer Exponents Use bases and exponents. Evaluate exponential expressions. Apply the product, quotient, and power rules. Polynomial Expressions Perform addition

### 4-9 Using Similar Figures. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up Solve each proportion. 1. k 4 = 75 25 3. k = 12 2. 6 19 = 24 x = 76 x Triangles JNZ and KOA are similar. Identify the side that corresponds

### MATH ALGEBRA AND FUNCTIONS

Students: 1. Use letters, boxes, or other symbols to stand for any number in simple expressions or equations. 1. Students use and interpret variables, mathematical symbols and properties to write and simplify

### Pre-Algebra Lesson Plans

EMS 8 th Grade Math Department Math Florida Standard(s): Learning Goal: Assessments Algebra Preview: Polynomials May 2 nd to June 3 rd, 2016 MAFS.912.A-SSE.1.1b (DOK 2) Interpret expressions that represent

### THE DISTRIBUTIVE LAW. Note: To avoid mistakes, include arrows above or below the terms that are being multiplied.

THE DISTRIBUTIVE LAW ( ) When an equation of the form a b c is epanded, every term inside the bracket is multiplied by the number or pronumeral (letter), and the sign that is located outside the brackets.

### 6-5 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

### Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1

8-7 Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Find each square root. 1. 6 2. 11 3. 25 4. Solve each equation. x = 10 5. 6x = 60 6. 7. 2x 40 = 0 8. 5x = 3 x = 20 x = 80 Objective Solve quadratic

Chapter 7 Polynomials Polynomials; Add/Subtract Polynomials sounds tough enough. But, if you look at it close enough you ll notice that students have worked with polynomial expressions such as 6x 2 + 5x

### Polynomials and Factoring

7.6 Polynomials and Factoring Basic Terminology A term, or monomial, is defined to be a number, a variable, or a product of numbers and variables. A polynomial is a term or a finite sum or difference of

### Algebra I. Slide 1 / 216. Slide 2 / 216. Slide 3 / 216. Polynomials

Slide 1 / 216 Slide 2 / 216 lgebra I Polynomials 2015-11-02 www.njctl.org Table of ontents efinitions of Monomials, Polynomials and egrees dding and Subtracting Polynomials Multiplying a Polynomial by

### mn 3 17x 2 81y 4 z Algebra I Definitions of Monomials, Polynomials and Degrees 32,457 Slide 1 / 216 Slide 2 / 216 Slide 3 / 216 Slide 4 / 216

Slide 1 / 216 Slide 2 / 216 lgebra I Polynomials 2015-11-02 www.njctl.org Slide 3 / 216 Table of ontents efinitions of Monomials, Polynomials and egrees dding and Subtracting Polynomials Multiplying a

### Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A4b & MM2A4c Time allotted for this Lesson: 9 hours

Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A4b & MM2A4c Time allotted for this Lesson: 9 hours Essential Question: LESSON 3 Solving Quadratic Equations and Inequalities

### CAHSEE on Target UC Davis, School and University Partnerships

UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 2006 Director Sarah R. Martinez,

### Algebraic Expressions and Identities

ALGEBRAIC EXPRESSIONS AND IDENTITIES 137 Algebraic Expressions and Identities CHAPTER 9 9.1 What are Expressions? In earlier classes, we have already become familiar with what algebraic expressions (or

### Grade 7 Math LESSON 23: MULTIPLYING POLYNOMIALS

GRADE 7 MATH Lesson 23: Multiplying Polynomials Time: 3 hours Pre-requisite Concepts: Laws of eponents, Adding and Subtracting Polynomials, Distributive Property of Real Numbers About the Lesson: In this

### Algebra Review C H A P T E R. To solve an algebraic equation with one variable, find the value of the unknown variable.

C H A P T E R 6 Algebra Review This chapter reviews key skills and concepts of algebra that you need to know for the SAT. Throughout the chapter are sample questions in the style of SAT questions. Each

Then You simplified radical expressions. (Lesson 10-2) Now 1Add and subtract radical expressions. 2Multiply radical expressions. Operations with Radical Expressions Why? Conchita is going to run in her

### Adding and Subtracting Polynomials Polynomials in the Sun

Adding and Subtracting Polynomials SUGGESTED LEARNING STRATEGIES: Shared Reading, Questioning the Text, Create Representations, Vocabulary Organizer, Note Taking A solar panel is a device that collects

### LESSON 9.1 ROOTS AND RADICALS

LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical

### Section 10-1: Laws of Exponents

Section -: Laws of Eponents Learning Outcome Multiply: - ( ) = - - = = To multiply like bases, add eponents, and use common base. Rewrite answer with positive eponent. Learning Outcome Write the reciprocals

### = 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

### A Five Day Exploration of Polynomials Using Algebra Tiles and the TI-83 Plus Graphing Calculator

Page 1. A Five Day Exploration of Polynomials Using Algebra Tiles and the TI-83 Plus Graphing Calculator Pre- Algebra Grade Seven By: Cory Savard Page. Overall Unit Objectives Upon completion of this unit,

### Ch. 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.

### Which of the following expressions are monomials?

9 1 Stud Guide Pages 382 387 Polnomials The epressions, 6, 5a 2, and 10cd 3 are eamples of monomials. A monomial is a number, a variable, or a product of numbers and variables. An eponents in a monomial

### Algebra 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

### 1Factor binomials that. 2Use the difference. Then. Why? Now. New Vocabulary dif ference of two squares

Then You factored trinomials into two binomials. (Lesson 8-3, 8-) New Vocabulary dif ference of two squares Now Quadratic Equations: Differences of Squares 1Factor binomials that are the difference of

### Algebra 2 (3) Apex - Semester 1 Part A

Algebra 2 (3) Apex - Semester 1 Part A Name Algebra I Literacy Advantage Unit 1 : The Need to Read Lesson 1.1 : Reading and Vocabulary Activity 1.1.1 : Study - Active Reading Learn skills and strategies

### Mission 1 Factoring by Greatest Common Factor and Grouping

Algebra Honors Unit 3 Factoring Quadratics Name Quest Mission 1 Factoring by Greatest Common Factor and Grouping Review Questions 1. Simplify: i(6 4i) 3+3i A. 4i C. 60 + 3 i B. 8 3 + 4i D. 10 3 + 3 i.

### Algebra Notes Quadratic Functions and Equations Unit 08

Note: This Unit contains concepts that are separated for teacher use, but which must be integrated by the completion of the unit so students can make sense of choosing appropriate methods for solving quadratic

### Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2

Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 April 11, 2016 Chapter 10 Section 1: Addition and Subtraction of Polynomials A monomial is

### A Add, subtract, multiply, and simplify polynomials and rational expressions.

ED 337 Paul Garrett Selected Response Assessment 10 th Grade Mathematics Examination Algebra II Clear Purpose: The purpose of this selected response is to ensure an understanding of expressions, manipulation

### SUMMER MATH PACKET ALGEBRA TWO COURSE 229

SUMMER MATH PACKET ALGEBRA TWO COURSE 9 MATH SUMMER PACKET INSTRUCTIONS MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The

### 16x y 8x. 16x 81. U n i t 3 P t 1 H o n o r s P a g e 1. Math 3 Unit 3 Day 1 - Factoring Review. I. Greatest Common Factor GCF.

P a g e 1 Math 3 Unit 3 Day 1 - Factoring Review I. Greatest Common Factor GCF Eamples: A. 3 6 B. 4 8 4 C. 16 y 8 II. Difference of Two Squares Draw ( - ) ( + ) Square Root 1 st and Last Term Eamples:

### Essential Question How can you cube a binomial? Work with a partner. Find each product. Show your steps. = (x + 1) Multiply second power.

4.2 Adding, Subtracting, and Multiplying Polynomials COMMON CORE Learning Standards HSA-APR.A.1 HSA-APR.C.4 HSA-APR.C.5 Essential Question How can you cube a binomial? Cubing Binomials Work with a partner.

### Algebra 1 Skills Needed for Success in Math

Algebra 1 Skills Needed for Success in Math A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed to simplif

### Math 75 Mini-Mod Due Dates Spring 2016

Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing

### Controlling the Population

Lesson.1 Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term. 1. polynomial a. a polynomial with only 1

### CP Algebra 2 Unit 2-1: Factoring and Solving Quadratics WORKSHEET PACKET

CP Algebra Unit -1: Factoring and Solving Quadratics WORKSHEET PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor