6-4 Adding and Subtracting Polynomials 6-4. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 1 1Algebra 1
|
|
|
- Louise Jacobs
- 6 years ago
- Views:
Transcription
1 6-4 Adding and Subtracting Polynomials Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 1Algebra 1
2 Warm Up Simplify each expression by combining like terms. 1. 4x + 2x 2. 3y + 7y 3. 8p 5p 6x 10y 3p 4. 5n + 6n 2 not like terms Simplify each expression. 5. 3(x + 4) 3x (t + 3) 2t (x 2 4x 6) x 2 + 4x + 6 Holt McDougal Algebra 1
3 Objective Add and subtract polynomials.
4 Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.
5 Example 1: Adding and Subtracting Monomials Add or subtract. A. 12p p 2 + 8p 3 12p p 2 + 8p 3 12p 3 + 8p p 2 20p p 2 B. 5x 2 6 3x + 8 5x 2 6 3x + 8 5x 2 3x x 2 3x + 2 Rearrange terms so that like terms are together. Rearrange terms so that like terms are together.
6 Example 1: Adding and Subtracting Monomials Add or subtract. C. t 2 + 2s 2 4t 2 s 2 t 2 + 2s 2 4t 2 s 2 t 2 4t 2 + 2s 2 s 2 3t 2 + s 2 Rearrange terms so that like terms are together. D. 10m 2 n + 4m 2 n 8m 2 n 10m 2 n + 4m 2 n 8m 2 n 6m 2 n
7 Remember! Like terms are constants or terms with the same variable(s) raised to the same power(s). To review combining like terms, see lesson 1-7.
8 Check It Out! Example 1 Add or subtract. a. 2s 2 + 3s 2 + s 2s 2 + 3s 2 + s 5s 2 + s b. 4z z z z z z z 4 6 Rearrange terms so that like terms are together.
9 Check It Out! Example 1 Add or subtract. c. 2x 8 + 7y 8 x 8 y 8 2x 8 + 7y 8 x 8 y 8 2x 8 x 8 + 7y 8 y 8 x 8 + 6y 8 Rearrange terms so that like terms are together. d. 9b 3 c 2 + 5b 3 c 2 13b 3 c 2 9b 3 c 2 + 5b 3 c 2 13b 3 c 2 b 3 c 2
10 Polynomials can be added in either vertical or horizontal form. In vertical form, align the like terms and add: 5x 2 + 4x x 2 + 5x + 2 7x 2 + 9x + 3 In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms. (5x 2 + 4x + 1) + (2x 2 + 5x + 2) = (5x 2 + 2x 2 ) + (4x + 5x) + (1 + 2) = 7x 2 + 9x + 3
11 Example 2: Adding Polynomials Add. A. (4m 2 + 5) + (m 2 m + 6) (4m 2 + 5) + (m 2 m + 6) (4m 2 + m 2 ) + ( m) +(5 + 6) 5m 2 m + 11 B. (10xy + x) + ( 3xy + y) (10xy + x) + ( 3xy + y) (10xy 3xy) + x + y 7xy + x + y Group like terms together. Group like terms together.
12 Example 2C: Adding Polynomials Add. (6x 2 4y) + (3x 2 + 3y 8x 2 2y) (6x 2 4y) + (3x 2 + 3y 8x 2 2y) (6x 2 4y) + ( 5x 2 + y) (6x 2 5x 2 ) + ( 4y + y) x 2 3y Combine like terms in the second polynomial. Simplify.
13 Add. Example 2D: Adding Polynomials Group like terms together.
14 Check It Out! Example 2 Add (5a 3 + 3a 2 6a + 12a 2 ) + (7a 3 10a). (5a 3 + 3a 2 6a + 12a 2 ) + (7a 3 10a) (5a 3 + 7a 3 ) + (3a a 2 ) + ( 10a 6a) 12a a 2 16a Group like terms together. Combine like terms
15 To subtract polynomials, remember that subtracting is the same as adding the opposite. To find the opposite of a polynomial, you must write the opposite of each term in the polynomial: (2x 3 3x + 7)= 2x 3 + 3x 7
16 Example 3A: Subtracting Polynomials Subtract. (x 3 + 4y) (2x 3 ) (x 3 + 4y) + ( 2x 3 ) (x 3 + 4y) + ( 2x 3 ) (x 3 2x 3 ) + 4y x 3 + 4y Rewrite subtraction as addition of the opposite. Group like terms together.
17 Example 3B: Subtracting Polynomials Subtract. (7m 4 2m 2 ) (5m 4 5m 2 + 8) (7m 4 2m 2 ) + ( 5m 4 + 5m 2 8) (7m 4 2m 2 ) + ( 5m 4 + 5m 2 8) Rewrite subtraction as addition of the opposite. (7m 4 5m 4 ) + ( 2m 2 + 5m 2 ) 8 Group like terms together. 2m 4 + 3m 2 8
18 Example 3C: Subtracting Polynomials Subtract. ( 10x 2 3x + 7) (x 2 9) ( 10x 2 3x + 7) + ( x 2 + 9) ( 10x 2 3x + 7) + ( x 2 + 9) 10x 2 3x + 7 x 2 + 0x x 2 3x + 16 Rewrite subtraction as addition of the opposite. Use the vertical method. Write 0x as a placeholder.
19 Example 3D: Subtracting Polynomials Subtract. (9q 2 3q) (q 2 5) (9q 2 3q) + ( q 2 + 5) (9q 2 3q) + ( q 2 + 5) 9q 2 3q q 2 0q + 5 8q 2 3q + 5 Rewrite subtraction as addition of the opposite. Use the vertical method. Write 0 and 0q as placeholders.
20 Check It Out! Example 3 Subtract. (2x 2 3x 2 + 1) (x 2 + x + 1) (2x 2 3x 2 + 1) + ( x 2 x 1) (2x 2 3x 2 + 1) + ( x 2 x 1) x 2 + 0x x 2 x 1 2x 2 x Rewrite subtraction as addition of the opposite. Use the vertical method. Write 0x as a placeholder.
21 Example 4: Application A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x 2 + 7x 5 and the area of plot B can be represented by 5x 2 4x Write a polynomial that represents the total area of both plots of land. (3x 2 + 7x 5) + (5x 2 4x + 11) 8x 2 + 3x + 6 Plot A. Plot B.
22 Check It Out! Example 4 The profits of two different manufacturing plants can be modeled as shown, where x is the number of units produced at each plant. Use the information above to write a polynomial that represents the total profits from both plants x x x x x x 3200 Eastern plant profit. Southern plant profit.
23 Add or subtract. Lesson Quiz: Part I 1. 7m 2 + 3m + 4m 2 11m 2 + 3m 2. (r 2 + s 2 ) (5r 2 + 4s 2 ) ( 4r 2 3s 2 ) 3. (10pq + 3p) + (2pq 5p + 6pq) 18pq 2p 4. (14d 2 8) + (6d 2 2d +1) 20d 2 2d 7 5. (2.5ab + 14b) ( 1.5ab + 4b) 4ab + 10b
24 Lesson Quiz: Part II 6. A painter must add the areas of two walls to determine the amount of paint needed. The area of the first wall is modeled by 4x x + 9, and the area of the second wall is modeled by 36x 2 12x + 1. Write a polynomial that represents the total area of the two walls. 40x
7-6 Adding and Subtracting Polynomials
Example 1: Adding and Subtracting Monomials Add or Subtract.. A. 12p 3 + 11p 2 + 8p 3 12p 3 + 11p 2 + 8p 3 12p 3 + 8p 3 + 11p 2 20p 3 + 11p 2 B. 5x 2 6 3x + 8 5x 2 6 3x + 8 5x 2 3x + 8 6 5x 2 3x + 2 Rearrange
I CAN classify polynomials by degree and by the number of terms.
13-1 Polynomials I CAN classify polynomials by degree and by the number of terms. 13-1 Polynomials Insert Lesson Title Here Vocabulary monomial polynomial binomial trinomial degree of a polynomial 13-1
17.2 Adding Polynomial Expressions
17.2 Adding Polynomial Expressions Essential Question: How do you add polynomials Explore Key ing Polynomial Addition Using Tiles Resource Locker You have added numbers and variables, which is the same
4.2 Adding Polynomial Expressions
Name Class Date 4.2 Adding Polynomial Expressions Essential Question: How do you add polynomials? Explore Key Modeling Polynomial Addition Using Algebra Tiles You have added numbers and variables, which
Topic 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
Ready 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:
Day 131 Practice. What Can You Do With Polynomials?
Polynomials Monomial - a Number, a Variable or a PRODUCT of a number and a variable. Monomials cannot have radicals with variables inside, quotients of variables or variables with negative exponents. Degree
2.4 Multiply Real Numbers
24 Multiply Real Numbers Goal p Multiply real numbers Your Notes VOCABULARY Multiplicative identity THE SIGN OF A PRODUCT The product of two real numbers with the same sign is Examples: 5(2) 5 24(25) 5
8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors
8-1 Factors and Greatest Common Factors Warm Up Lesson Presentation Lesson Quiz 1 2 pts 2 pts Bell Quiz 8-1 Tell whether the second number is a factor of the first number 1. 50, 6 2 pts no 2. 105, 7 3.
Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 2
Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Factor each expression. 1. 3x 6y 2. a 2 b 2 3(x 2y) (a + b)(a b) Find each product. 3. (x 1)(x + 3) 4. (a + 1)(a 2 + 1) x 2 + 2x 3 a 3 + a 2 +
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
5.2. Adding and Subtracting Polynomials. Objectives. Know the basic definitions for polynomials. Add and subtract polynomials.
Chapter 5 Section 2 5.2 Adding and Subtracting Polynomials Objectives 1 2 Know the basic definitions for polynomials. Add and subtract polynomials. Objective 1 Know the basic definitions for polynomials.
Review 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
Lesson 3: Polynomials and Exponents, Part 1
Lesson 2: Introduction to Variables Assessment Lesson 3: Polynomials and Exponents, Part 1 When working with algebraic expressions, variables raised to a power play a major role. In this lesson, we look
Teacher's Page. Mar 20 8:26 AM
Teacher's Page Unit 4.1 in two parts: Part 1: Polynomials and Part 2: Quadratics Benchmarks: A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity
Standards Lesson Notes
8.2 Add and Subtract Polynomials ink.notebook Page 61 page 62 8.2 Add and Subtract Polynomials Lesson Objectives Standards Lesson Objectives Standards Lesson Notes Lesson Notes A.SSE.2 I will rewrite a
6-3 Solving Systems by Elimination
Another method for solving systems of equations is elimination. Like substitution, the goal of elimination is to get one equation that has only one variable. To do this by elimination, you add the two
EXAMPLE 1. a. Add 2x 3 5x 2 + 3x 9 and x 3 + 6x in a vertical format. SOLUTION. a. 2x 3 5x 2 + 3x 9 + x 3 + 6x x 3 + x 2 + 3x + 2
EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x 3 5x 2 + 3x 9 and x 3 + 6x 2 + 11 in a vertical format. a. 2x 3 5x 2 + 3x 9 + x 3 + 6x 2 + 11 3x 3 + x 2 + 3x + 2 EXAMPLE 1 Add polynomials
3.4 Solve Equations with Variables
3.4 Solve Equations with Variables on Both Sides Goal p Solve equations with variables on both sides. Your Notes VOCABULARY Identity Example 1 Solve 15 1 4a 5 9a 2 5. Solve an equation with variables on
LESSON 8.1 RATIONAL EXPRESSIONS I
LESSON 8. RATIONAL EXPRESSIONS I LESSON 8. RATIONAL EXPRESSIONS I 7 OVERVIEW Here is what you'll learn in this lesson: Multiplying and Dividing a. Determining when a rational expression is undefined Almost
5-3 Solving Systems by Elimination
5-3 Solving Systems by Elimination Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Simplify each expression. 1. 3x + 2y 5x 2y 2x 2. 5(x y) + 2x + 5y 7x 3. 4y + 6x 3(y + 2x) 4. 2y 4x 2(4y 2x)
Exponents and Polynomials. (5) Page 459 #15 43 Second Column; Page 466 #6 30 Fourth Column
Algebra Name: Date: Period: # Exponents and Polynomials (1) Page 453 #22 59 Left (2) Page 453 #25 62 Right (3) Page 459 #5 29 Odd (4) Page 459 #14 42 First Column; Page 466 #3 27 First Column (5) Page
Unit 13: Polynomials and Exponents
Section 13.1: Polynomials Section 13.2: Operations on Polynomials Section 13.3: Properties of Exponents Section 13.4: Multiplication of Polynomials Section 13.5: Applications from Geometry Section 13.6:
Warm Up Lesson Presentation Lesson Quiz. Holt Algebra McDougal 1 Algebra 1
1-3 Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Evaluate each expression. 1. ( 7)(2.8) 19. 2. 0.9 3. ( 9)( 9) 0.1 81 4. 5.. 1 2 3 1.8 Objective Solve one-step equations
Sect Addition and Subtraction of Polynomials
Sect 5.5 - Addition and Subtraction of Polynomials Concept #1 Introduction to Polynomials Before we begin discussing polynomials, let s review some items from chapter 1 with the following example: Complete
MA 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
We say that a polynomial is in the standard form if it is written in the order of decreasing exponents of x. Operations on polynomials:
R.4 Polynomials in one variable A monomial: an algebraic expression of the form ax n, where a is a real number, x is a variable and n is a nonnegative integer. : x,, 7 A binomial is the sum (or difference)
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
2-4. Warm Up Lesson Presentation Lesson Quiz
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Solve each equation. 1. 2x 5 = 17 6 2. 14 Solve each inequality and graph the solutions. 3. 5 < t + 9 t > 4 4. a 8 Objective
Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions.
Lesson Objectives: Students will be able to define, recognize and use the following terms in the context of polynomials: o Constant o Variable o Monomial o Binomial o Trinomial o Polynomial o Numerical
2-5 Solving Equations Containing Integers. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up Use mental math to find each solution. 1. 7 + y = 15 2. x 9 = 9 3. 6x = 24 4. x 12 = 30 Problem of the Day Zelda sold her wet suit
UNIT 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
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
LESSON 6.2 POLYNOMIAL OPERATIONS I
LESSON 6. POLYNOMIAL OPERATIONS I LESSON 6. POLYNOMIALS OPERATIONS I 63 OVERVIEW Here's what you'll learn in this lesson: Adding and Subtracting a. Definition of polynomial, term, and coefficient b. Evaluating
Properties of Real Numbers
Properties of Real Numbers Essential Understanding. Relationships that are always true for real numbers are called properties, which are rules used to rewrite and compare expressions. Two algebraic expressions
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
Sections 7.1, 7.2: Sums, differences, products of polynomials CHAPTER 7: POLYNOMIALS
Sections 7.1, 7.2: Sums, differences, products of polynomials CHAPTER 7: POLYNOMIALS Quiz results Average 73%: high h score 100% Problems: Keeping track of negative signs x = + = + Function notation f(x)
Collecting 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.
A-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
Lesson 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
Introduction. Adding and Subtracting Polynomials
Introduction Polynomials can be added and subtracted like real numbers. Adding and subtracting polynomials is a way to simplify expressions. It can also allow us to find a shorter way to represent a sum
4.6 Model Direct Variation
4.6 Model Direct Variation Goal p Write and graph direct variation equations. Your Notes VOCABULARY Direct variation Constant of variation Eample Identif direct variation equations Tell whether the equation
LESSON 6.2 POLYNOMIAL OPERATIONS I
LESSON 6.2 POLYNOMIAL OPERATIONS I Overview In business, people use algebra everyday to find unknown quantities. For example, a manufacturer may use algebra to determine a product s selling price in order
Review: 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
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
Pre-Algebra Notes Unit 12: Polynomials and Sequences
Pre-Algebra Notes Unit 1: Polynomials and Sequences Polynomials Syllabus Objective: (6.1) The student will write polynomials in standard form. Let s review a definition: monomial. A monomial is a number,
How can you factor the trinomial x 2 + bx + c into the product of two binomials? ACTIVITY: Finding Binomial Factors
7.7 Factoring x 2 + bx + c How can you factor the trinomial x 2 + bx + c into the product of two binomials? 1 ACTIVITY: Finding Binomial Factors Work with a partner. Six different algebra tiles are shown
Inverse Variation. y varies inversely as x. REMEMBER: Direct variation y = kx where k is not equal to 0.
Inverse Variation y varies inversely as x. REMEMBER: Direct variation y = kx where k is not equal to 0. Inverse variation xy = k or y = k where k is not equal to 0. x Identify whether the following functions
Polynomial Operations
Chapter 7 Polynomial Operations Sec. 1 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
(2 x 2-3x + 5) + ( x 2 + 6x - 4) = 3 x 2 + 3x + 1 (continued on the next page)
Algebra Lab Adding and Subtracting Polynomials Monomials such as 3x and -x are called like terms because they have the same variable to the same power. When you use algebra tiles, you can recognize like
Order of Operations Practice: 1) =
Order of Operations Practice: 1) 24-12 3 + 6 = a) 6 b) 42 c) -6 d) 192 2) 36 + 3 3 (1/9) - 8 (12) = a) 130 b) 171 c) 183 d) 4,764 1 3) Evaluate: 12 2-4 2 ( - ½ ) + 2 (-3) 2 = 4) Evaluate 3y 2 + 8x =, when
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
Factor each expression. Remember, always find the GCF first. Then if applicable use the x-box method and also look for difference of squares.
NOTES 11: RATIONAL EXPRESSIONS AND EQUATIONS Name: Date: Period: Mrs. Nguyen s Initial: LESSON 11.1 SIMPLIFYING RATIONAL EXPRESSIONS Lesson Preview Review Factoring Skills and Simplifying Fractions Factor
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
Ready To Go On? Skills Intervention 6-1 Polynomials
6A Read To Go On? Skills Intervention 6- Polnomials Find these vocabular words in Lesson 6- and the Multilingual Glossar. Vocabular monomial polnomial degree of a monomial degree of a polnomial leading
Variables and Expressions
Variables and Expressions A variable is a letter that represents a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic
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
Polynomials. Exponents. End Behavior. Writing. Solving Factoring. Graphing. End Behavior. Polynomial Notes. Synthetic Division.
Polynomials Polynomials 1. P 1: Exponents 2. P 2: Factoring Polynomials 3. P 3: End Behavior 4. P 4: Fundamental Theorem of Algebra Writing real root x= 10 or (x+10) local maximum Exponents real root x=10
review To find the coefficient of all the terms in 15ab + 60bc 17ca: Coefficient of ab = 15 Coefficient of bc = 60 Coefficient of ca = -17
1. Revision Recall basic terms of algebraic expressions like Variable, Constant, Term, Coefficient, Polynomial etc. The coefficients of the terms in 4x 2 5xy + 6y 2 are Coefficient of 4x 2 is 4 Coefficient
A field trips costs $800 for the charter bus plus $10 per student for x students. The cost per student is represented by: 10x x
LEARNING STRATEGIES: Activate Prior Knowledge, Shared Reading, Think/Pair/Share, Note Taking, Group Presentation, Interactive Word Wall A field trips costs $800 for the charter bus plus $10 per student
5.3. Polynomials and Polynomial Functions
5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a
6. 2 Multiplying Polynomials
Name Class Date 6. 2 Multiplying Polynomials Essential Question: How do you multiply polynomials, and what type of expression is the result? Explore Analyzing a Visual Model for Polynomial Multiplication
LESSON 13.1 NONLINEAR EQUATIONS
LESSON. NONLINEAR EQUATIONS LESSON. NONLINEAR EQUATIONS 58 OVERVIEW Here's what you'll learn in this lesson: Solving Equations a. Solving polynomial equations by factoring b. Solving quadratic type equations
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
Solving Equations by Multiplying or Dividing
2-2 Warm Up Lesson Presentation Lesson Quiz Bell Quiz 2-2 3 pts Solve each equation. Check your answer. 1. u -15 = -8 3 pts 3 pts 2. 19 + a = 19 3. -12 + f = 3 10 pts possible 1 pt for putting your name
Adding and Subtracting Polynomials
7.2 Adding and Subtracting Polynomials subtract polynomials? How can you add polynomials? How can you 1 EXAMPLE: Adding Polynomials Using Algebra Tiles Work with a partner. Six different algebra tiles
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
6-3 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
Properties of Real Numbers. Unit 1 Lesson 4
Properties of Real Numbers Unit 1 Lesson 4 Students will be able to: Recognize and use the properties of real numbers. Key Vocabulary: Identity Property Inverse Property Equality Property Associative Property
Student Instruction Sheet: Unit 1 Lesson 3. Polynomials
Student Instruction Sheet: Unit 1 Lesson 3 Suggested time: 150 min Polynomials What s important in this lesson: You will use algebra tiles to learn how to add/subtract polynomials. Problems are provided
LESSON EII.F ABSOLUTE VALUE 89
LESSON EII.F ABSOLUTE VALUE LESSON EII.F ABSOLUTE VALUE 89 OVERVIEW Here s what you ll learn in this lesson: Solving Equations a. Solving x = a b. Solving Ax + B = a c. Solving Ax + B = Cx + D Solving
20A. Build. Build and add. Build a rectangle and find the area (product). l e s s o n p r a c t i c e 1. X X X 2 + 6X X
l e s s o n p r a c t i c e 0A Build.. X X. X 6X 8 3. X 8 Build and add. 4. X 6X 3 3X 7X 9 5. X 8 X 6X 7 6. X 0X 7 X 8X 9 Build a rectangle and find the area (product). 7. (X )(X ) = 8. (X 4)(X 3) = 9.
Adding & Subtracting Polynomial Expressions
Adding & Subtracting Polynomial Expressions A polynomial is a single term or the sum of two or more terms containing variables with exponents that are positive integers. Polynomials are ADDED or SUBTRACTED
Overview (90 Days) Properties of Equality Properties of Inequality Solve Linear Function
Pre- Requisites Skills: Overview (90 Days) Students need to know the meanings of exponents (2 4 = 2 2 2 2) Students need to know how to graph a simple inequality on a number line (i.e. x > 4) Students
Algebra 2 Summer Math Answer Section
Algebra 2 Summer Math Answer Section 1. ANS: A PTS: 1 DIF: Level B REF: MALG0064 STA: SC.HSCS.MTH.00.AL1.A1.I.C.4 TOP: Lesson 1.1 Evaluate Expressions KEY: word volume cube area solid 2. ANS: C PTS: 1
Lesson 2 - Mini-Lesson. Section 2.1 Properties of Exponents
Lesson - Mini-Lesson Section.1 Properties of Exponents What is an exponent? An exponent is a number in the superscript location and identifies the number of times the base number is to be multiplied times
TEKS: 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
Reteach Simplifying Algebraic Expressions
1-4 Simplifying Algebraic Expressions To evaluate an algebraic expression you substitute numbers for variables. Then follow the order of operations. Here is a sentence that can help you remember the order
1. Division by a Monomial
330 Chapter 5 Polynomials Section 5.3 Concepts 1. Division by a Monomial 2. Long Division 3. Synthetic Division Division of Polynomials 1. Division by a Monomial Division of polynomials is presented in
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
Unit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating
Hart Interactive Math Algebra 1 MODULE 2 An algebraic expression that can contains 1 Algebraic Expression variables, numbers and operators (like +,, x and ). 1 Equation An equation is a math sentence stating
Polynomial Operations
Chapter 7 Polynomial Operations Sec. 1 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
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
Solving Linear Equations
Solving Linear Equations Golden Rule of Algebra: Do unto one side of the equal sign as you will do to the other Whatever you do on one side of the equal sign, you MUST do the same exact thing on the other
Solving Equations Quick Reference
Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number
Classifying Polynomials. Simplifying Polynomials
1 Classifying Polynomials A polynomial is an algebraic expression with one or more unlike terms linked together by + or **Polynomials can be classified by the number of terms they have: A monomial has
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
Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Algebra 2
4-5 Warm Up Lesson Presentation Lesson Quiz Algebra 2 Warm Up Solve. 1. log 16 x = 3 2 64 2. log x 1.331 = 3 1.1 3. log10,000 = x 4 Objectives Solve exponential and logarithmic equations and equalities.
Math 154 :: Elementary Algebra
Math :: Elementar Algebra Section. Section. Section. Section. Section. Section. Math :: Elementar Algebra Section. Eponents. When multipling like-bases, ou can add the eponents to simplif the epression..
Chapter 3-1 Polynomials
Chapter 3 notes: Chapter 3-1 Polynomials Obj: SWBAT identify, evaluate, add, and subtract polynomials A monomial is a number, a variable, or a product of numbers and variables with whole number exponents
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
Reteach Multiplying and Dividing Rational Expressions
8-2 Multiplying and Dividing Rational Expressions Examples of rational expressions: 3 x, x 1, and x 3 x 2 2 x 2 Undefined at x 0 Undefined at x 0 Undefined at x 2 When simplifying a rational expression:
Lesson 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.
Algebra Review. Terrametra Resources. Lynn Patten
Terrametra Resources Lynn Patten ALGEBRAIC EXPRESSION A combination of ordinary numbers, letter symbols, variables, grouping symbols and operation symbols. Numbers remain fixed in value and are referred
Adding and Subtracting Terms
Adding and Subtracting Terms 1.6 OBJECTIVES 1.6 1. Identify terms and like terms 2. Combine like terms 3. Add algebraic expressions 4. Subtract algebraic expressions To find the perimeter of (or the distance
Alg 1B Chapter 7 Final Exam Review
Name: Class: Date: ID: A Alg B Chapter 7 Final Exam Review Please answer all questions and show your work. Simplify ( 2) 4. 2. Simplify ( 4) 4. 3. Simplify 5 2. 4. Simplify 9x0 y 3 z 8. 5. Simplify 7w0
correlated to the Washington D.C. Public Schools Learning Standards Algebra I
correlated to the Washington D.C. Public Schools Learning Standards Algebra I McDougal Littell Algebra 1 2007 correlated to the Washington DC Public Schools Learning Standards Algebra I NUMBER SENSE AND
Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1
Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Chapter 5 Lesson 1 Use Properties of Exponents Vocabulary Learn these! Love these! Know these! 1 Example 1: Evaluate Numerical Expressions
5 3w. Unit 2 Function Operations and Equivalence Standard 4.1 Add, Subtract, & Multiply Polynomials
Unit Function Operations and Equivalence This document is meant to be used as an eample guide for each of the skills we will be holding students accountable for with Standard 4.1. This document should
LESSON 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 +