# Maintaining Mathematical Proficiency

Size: px
Start display at page:

Transcription

1 Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t s 4 + 4s 6 5s 4. 9m m 3 + 5m p 7 3p 4 1 z ( ) 7. 6( x + ) ( h + 4) 3( h 4) 9. 7( z + 4) 3( z + ) ( z 3) Find the greatest common factor , , , , , , Explain how to find the greatest common factor of 4, 70, and

2 Name Date 7.1 Adding and Subtracting Polynomials For use with Exploration 7.1 Essential Question How can you add and subtract polynomials? 1 EXPLORATION: Adding Polynomials Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Write the expression modeled by the algebra tiles in each step. Step 1 + ( 3x + ) + ( x 5) Step Step 3 Step 4 EXPLORATION: Subtracting Polynomials Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Write the expression modeled by the algebra tiles in each step. Step 1 ( x + x + ) ( x 1 ) Step + Step 3 04 Algebra 1 Copyright Big Ideas Learning, LLC

3 7.1 Adding and Subtracting Polynomials (continued) EXPLORATION: Subtracting Polynomials (continued) Step 4 Step 5 Communicate Your Answer 3. How can you add and subtract polynomials? 4. Use your methods in Question 3 to find each sum or difference b. ( 4x + 3) + ( x ) a. ( x x 1) ( x x 1) c. ( x + ) ( 3x + x + 5) d. ( x 3x) ( x x + 4) 05

4 Name Date 7.1 Notetaking with Vocabulary For use after Lesson 7.1 In your own words, write the meaning of each vocabulary term. monomial degree of a monomial polynomial binomial trinomial degree of a polynomial standard form leading coefficient closed Notes: 06 Algebra 1 Copyright Big Ideas Learning, LLC

5 7.1 Notetaking with Vocabulary (continued) Core Concepts Polynomials A polynomial is a monomial or a sum of monomials. Each monomial is called a term of the polynomial. A polynomial with two terms is a binomial. A polynomial with three terms is a trinomial. Binomial Trinomial 5x + x + 5x + The degree of a polynomial is the greatest degree of its terms. A polynomial in one variable is in standard form when the exponents of the terms decrease from left to right. When you write a polynomial in standard form, the coefficient of the first term is the leading coefficient. leading coefficient degree x 3 + x 5x + 1 constant term Notes: Extra Practice In Exercises 1 8, find the degree of the monomial. 1. 6s. w abc x y 6. 4r st 7. 10mn

6 Name Date 7.1 Notetaking with Vocabulary (continued) In Exercises 9 1, write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms x + 3x y 11. 3x + 6x 1. f f + f In Exercises 13 16, find the sum. 13. ( 4x + 9) + ( 6x 14) 14. ( 3a ) + ( 7a + 5) 15. ( x + 3x + 5) + ( x + 6x 4) 16. ( t + 3t 3 3) + ( t + 7t t 3 ) In Exercises 17 0, find the difference. 17. ( g 4) ( 3g 6) 18. ( 5h ) ( 7h + 6) 19. ( x 5) ( 3x x 8) 0. ( k + 6k 3 4) ( 5k 3 + 7k 3k ) 08 Algebra 1 Copyright Big Ideas Learning, LLC

7 7. Multiplying Polynomials For use with Exploration 7. Essential Question How can you multiply two polynomials? 1 EXPLORATION: Multiplying Monomials Using Algebra Tiles Work with a partner. Write each product. Explain your reasoning. = = a. b. = = c. d. = = e. f. = = g. h. = = i. j. 09

8 Name Date 7. Multiplying Polynomials (continued) EXPLORATION: Multiplying Binomials Using Algebra Tiles Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Write the product of two binomials modeled by each rectangular array of algebra tiles. In parts (c) and (d), first draw the rectangular array of algebra tiles that models each product. a. ( x + 3)( x ) = b. ( x )( x ) = c. ( x + )( x 1 ) = d. ( x )( x ) 3 = Communicate Your Answer 3. How can you multiply two polynomials? 4. Give another example of multiplying two binomials using algebra tiles that is similar to those in Exploration. 10 Algebra 1 Copyright Big Ideas Learning, LLC

9 7. Notetaking with Vocabulary For use after Lesson 7. In your own words, write the meaning of each vocabulary term. FOIL Method Core Concepts FOIL Method To multiply two binomials using the FOIL Method, find the sum of the products of the First terms, (x + 1)(x + ) x(x) = x Outer terms, (x + 1)(x + ) x() = x Inner terms, and (x + 1)(x + ) 1(x) = x Last terms. (x + 1)(x + ) 1() = ( )( ) x + 1 x + = x + x + x + = x + 3x + Notes: 11

10 Name Date 7. Notetaking with Vocabulary (continued) Extra Practice In Exercises 1 6, use the Distributive Property to find the product. 1. ( x )( x 1). ( b 3)( b + ) 3. ( g + )( g + 4) 4. ( a 1)( a + 5) 5. ( 3n 4)( n + 1) 6. ( r + 3)( 3r + ) In Exercises 7 1, use a table to find the product. 7. ( x 3)( x ) 8. ( y + 1)( y 6) 9. ( q + 3)( q + 7) 10. ( w 5)( w 3) 11. ( 6h )( 3 h) 1. ( 3 + 4j)( 3j + 4) 1 Algebra 1 Copyright Big Ideas Learning, LLC

11 7. Notetaking with Vocabulary (continued) In Exercises 13 18, use the FOIL Method to find the product. 13. ( x + )( x 3) 14. ( z + 3)( z + ) 15. ( h )( h + 4) 16. ( m 1)( m + ) 17. ( 4n 1)( 3n + 4) 18. ( q 1)( q + 1) In Exercises 19 4, find the product. 19. ( x )( x + x 1) 0. ( a)( 3a + 3a 5) 1. ( h + 1)( h h 1). ( d 3)( d 4d 1) ( 3n + n 5)( n + 1) 4. ( p + p 3)( 3p 1) 13

12 Name Date 7.3 Special Products of Polynomials For use with Exploration 7.3 Essential Question What are the patterns in the special products a + b a b, a + b, and a b? ( )( ) ( ) ( ) 1 EXPLORATION: Finding a Sum and Difference Pattern Work with a partner. Write the product of two binomials modeled by each rectangular array of algebra tiles. a. ( x + )( x ) = b. ( x )( x ) = EXPLORATION: Finding the Square of a Binomial Pattern Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Draw the rectangular array of algebra tiles that models each product of two binomials. Write the product. a. ( x + ) = b. ( ) x 1 = 14 Algebra 1 Copyright Big Ideas Learning, LLC

13 7.3 Special Products of Polynomials (continued) Communicate Your Answer a + b a b, a + b, 3. What are the patterns in the special products ( )( ) ( ) and a ( b)? 4. Use the appropriate special product pattern to find each product. Check your answers using algebra tiles. a. ( x + 3)( x 3) b. ( x 4)( x + 4) c. ( 3x + 1)( 3x 1) d. ( x + 3) e. ( x ) f. ( 3x + 1) 15

14 Name Date 7.3 Notetaking with Vocabulary For use after Lesson 7.3 In your own words, write the meaning of each vocabulary term. binomial Core Concepts Square of a Binomial Pattern Algebra Example ( ) a b a ab b + = + + ( x + 5) = ( x) + ( x)( 5) + ( 5) = x + x ( ) a b = a ab + b ( x 3) = ( x) ( x)( 3) + ( 3) Notes: = + 4x 1x 9 Sum and Difference Pattern Algebra Example ( a + b)( a b) = a b ( x )( x ) x Notes: = 9 16 Algebra 1 Copyright Big Ideas Learning, LLC

15 7.3 Notetaking with Vocabulary (continued) Extra Practice In Exercises 1 18, find the product. 1. ( a + 3). ( b ) 3. ( c + 4) 4. ( x + 1) 5. ( 3x ) 6. ( 4p 3) 7. ( 3x + y ) 8. ( a 3b ) 9. ( 4c + 5d) 10. ( x 3)( x + 3) 11. ( q + 5)( q 5) 1. ( t 11)( t + 11) 17

16 Name Date 7.3 Notetaking with Vocabulary (continued) 13. ( 5 1)( 5 + 1) a a b + 1 b c + c ( m + n)( m n) 17. ( 3j k)( 3j k) a + b 6a + b In Exercises 19 4, use special product patterns to find the product ( 31 ) 3. ( 0.7 ) 4. ( 109 ) 5. Find k so that kx 1x + 9 is the square of a binomial. 18 Algebra 1 Copyright Big Ideas Learning, LLC

17 7.4 Solving Polynomial Equations in Factored Form For use with Exploration 7.4 Essential Question How can you solve a polynomial equation? 1 EXPLORATION: Matching Equivalent Forms of an Equation Work with a partner. An equation is considered to be in factored form when the product of the factors is equal to 0. Match each factored form of the equation with its equivalent standard form and nonstandard form. Factored Form Standard Form Nonstandard Form x 1 x 3 = 0 A. x x = 0 1. x 5x = 6 a. ( )( ) x x 3 = 0 B. + = 0 b. ( )( ) c. ( )( ) x x. ( x ) 1 = 4 x + 1 x = 0 C. x 4x + 3 = 0 3. x x = x 1 x + = 0 D = 0 d. ( )( ) x x 4. xx ( ) + 1 = x + 1 x 3 = 0 E. x x 3 = 0 5. e. ( )( ) x 4x = 3 EXPLORATION: Writing a Conjecture Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Substitute 1,, 3, 4, 5, and 6 for x in each equation and determine whether the equation is true. Organize your results in the table. Write a conjecture describing what you discovered. a. ( x )( x ) Equation x =1 x = x = 3 x = 4 x = 5 x = 6 1 = 0 b. ( x )( x ) 3 = 0 c. ( x )( x ) 3 4 = 0 d. ( x )( x ) 4 5 = 0 e. ( x )( x ) 5 6 = 0 f. ( x )( x ) 6 1 = 0 19

18 Name Date 7.4 Solving Polynomial Equations in Factored Form (continued) 3 EXPLORATION: Special Properties of 0 and 1 Work with a partner. The numbers 0 and 1 have special properties that are shared by no other numbers. For each of the following, decide whether the property is true for 0, 1, both, or neither. Explain your reasoning. a. When you add to a number n, you get n. b. If the product of two numbers is, then at least one of the numbers is 0. c. The square of is equal to itself. d. When you multiply a number n by, you get n. e. When you multiply a number n by, you get 0. f. The opposite of is equal to itself. Communicate Your Answer 4. How can you solve a polynomial equation? 5. One of the properties in Exploration 3 is called the Zero-Product Property. It is one of the most important properties in all of algebra. Which property is it? Why do you think it is called the Zero-Product Property? Explain how it is used in algebra and why it so important. 0 Algebra 1 Copyright Big Ideas Learning, LLC

19 7.4 Notetaking with Vocabulary For use after Lesson 7.4 In your own words, write the meaning of each vocabulary term. factored form Zero-Product Property roots repeated roots Core Concepts Zero-Product Property Words If the product of two real numbers is 0, then at least one of the numbers is 0. Algebra If a and b are real numbers and ab = 0, then a = 0 or b = 0. Notes: 1

20 Name Date 7.4 Notetaking with Vocabulary (continued) Extra Practice In Exercises 1 1, solve the equation. 1. xx+ ( 5) = 0. aa ( 1) = 0 3. ( ) 5pp = 0 4. ( c )( c + 1) = 0 5. ( b 6)( 3b + 18) = 0 6. ( s)( s) = 0 7. ( x 3) = 0 8. ( 3d + 7)( 5d 6) = 0 9. ( t )( t ) = ( w + 4) ( w + 1) = g( g)( g) + = 1. ( m )( m)( m) = 0 3 Algebra 1 Copyright Big Ideas Learning, LLC

21 7.4 Notetaking with Vocabulary (continued) In Exercises 13 18, factor the polynomial x + 3x 14. 4y 0y u 6u z + z 17. 4h + 8h f 45 f In Exercises 19 4, solve the equation k + k = n 49n = z + 5z = 0. 6x 7 = x 3. s = 11s 4. 7p = 1p 5. A boy kicks a ball in the air. The height y (in feet) above the ground of the ball is modeled by the equation y = 16x + 80 x, where x is the time (in seconds) since the ball was kicked. Find the roots of the equation when y = 0. Explain what the roots mean in this situation. 3

22 Name Date 7.5 Factoring x + bx + c For use with Exploration 7.5 Essential Question How can you use algebra tiles to factor the trinomial x + bx + c into the product of two binomials? 1 EXPLORATION: Finding Binomial Factors Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Use algebra tiles to write each polynomial as the product of two binomials. Check your answer by multiplying. Sample x + 5x + 6 Step 1 Arrange algebra tiles that Step model x + 5x + 6 into a rectangular array. Use additional algebra tiles to model the dimensions of the rectangle. Step 3 Write the polynomial in factored form using the dimensions of the rectangle. width length Area = x + 5x + 6 = (x + )(x + 3) a. x 3x + = b. x + 5x + 4 = 4 Algebra 1 Copyright Big Ideas Learning, LLC

23 7.5 Factoring x + bx + c (continued) 1 EXPLORATION: Finding Binomial Factors (continued) c. x 7x + 1 = d. x + 7x + 1 = Communicate Your Answer. How can you use algebra tiles to factor the trinomial x + bx + c into the product of two binomials? 3. Describe a strategy for factoring the trinomial x + bx + c that does not use algebra tiles. 5

24 Name Date 7.5 Notetaking with Vocabulary For use after Lesson 7.5 In your own words, write the meaning of each vocabulary term. polynomial FOIL Method Zero-Product Property Core Concepts Factoring x + bx + c When c Is Positive x + bx + c = x + p x + q when p + q = b and pq = c. When c is positive, p and q have the same sign as b. Algebra ( )( ) Examples x + 6x + 5 = ( x + 1)( x + 5) x 6x + 5 = ( x 1)( x 5) Notes: Factoring x + bx + c When c Is Negative x + bx + c = x + p x + q when p + q = b and pq = c. When c is negative, p and q have different signs. Algebra ( )( ) Example x 4 x 5 = ( x + 1 )( x 5 ) Notes: 6 Algebra 1 Copyright Big Ideas Learning, LLC

25 7.5 Notetaking with Vocabulary (continued) Extra Practice In Exercises 1 1, factor the polynomial. 1. c + 8c + 7. a + 16a x + 11x d + 6d s + 11s u + 10u b + 3b y y 9. u + 3u z z h + h 4 1. f 3f 40 7

26 Name Date 7.5 Notetaking with Vocabulary (continued) In Exercises 13 18, solve the equation. 13. g 13g + 40 = k 5k + 6 = w 7w + 10 = x x = r 3r = 18. t 7t = The area of a right triangle is 16 square miles. One leg of the triangle is 4 miles longer than the other leg. Find the length of each leg. 0. You have two circular flower beds, as shown. The sum of the areas of the two flower beds is 136 π square feet. Find the radius of each bed. 8 Algebra 1 Copyright Big Ideas Learning, LLC

27 7.6 Factoring ax + bx + c For use with Exploration 7.6 Essential Question How can you use algebra tiles to factor the trinomial + + ax bx c into the product of two binomials? 1 EXPLORATION: Finding Binomial Factors Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Use algebra tiles to write each polynomial as the product of two binomials. Check your answer by multiplying. Sample x + 5x + Step 1 Arrange algebra tiles that Step model x + 5x + into a rectangular array. Use additional algebra tiles to model the dimensions of the rectangle. Step 3 Write the polynomial in factored form using the dimensions of the rectangle. width Area = x + 5x + = (x + )(x + 1) length a. 3x + 5x + = 9

28 Name Date 7.6 Factoring ax + bx + c (continued) 1 EXPLORATION: Finding Binomial Factors (continued) b. 4x + 4x 3 = c. x 11x + 5 = Communicate Your Answer. How can you use algebra tiles to factor the trinomial ax + bx + c into the product of two binomials? 3. Is it possible to factor the trinomial x + x + 1? Explain your reasoning. 30 Algebra 1 Copyright Big Ideas Learning, LLC

29 7.6 Notetaking with Vocabulary For use after Lesson 7.6 In your own words, write the meaning of each vocabulary term. polynomial greatest common factor (GCF) Zero-Product Property Notes: 31

30 Name Date 7.6 Notetaking with Vocabulary (continued) Extra Practice In Exercises 1 18, factor the polynomial. 1. c 14c 36. 4a + 8a x 6x 4 4. d d s + 55s q + 30q g 37g k 11k w + 9w a + 5a b + 14b t + 1t 9 3 Algebra 1 Copyright Big Ideas Learning, LLC

31 7.6 Notetaking with Vocabulary (continued) 13. 1b + 5b x + x g 11g d d r 4r x 14x The length of a rectangular shaped park is ( 3x + 5) miles. The width is ( x + 8) The area of the park is 360 square miles. What are the dimensions of the park? miles. 0. The sum of two numbers is 8. The sum of the squares of the two numbers is 34. What are the two numbers? 33

32 Name Date 7.7 Factoring Special Products For use with Exploration 7.7 Essential Question How can you recognize and factor special products? 1 EXPLORATION: Factoring Special Products Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Use algebra tiles to write each polynomial as the product of two binomials. Check your answer by multiplying. State whether the product is a special product that you studied in Section 7.3. a. 4x 1 = b. 4x 4x + 1 = c. 4x 4x = d. 4x 6x + = 34 Algebra 1 Copyright Big Ideas Learning, LLC

33 7.7 Factoring Special Products (continued) EXPLORATION: Factoring Special Products Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Use algebra tiles to complete the rectangular arrays in three different ways, so that each way represents a different special product. Write each special product in standard form and in factored form. Communicate Your Answer 3. How can you recognize and factor special products? Describe a strategy for recognizing which polynomials can be factored as special products. 4. Use the strategy you described in Question 3 to factor each polynomial. a. 5x + 10x + 1 b. 5x 10x + 1 c. 5x 1 35

34 Name Date 7.7 Notetaking with Vocabulary For use after Lesson 7.7 In your own words, write the meaning of each vocabulary term. polynomial trinomial Core Concepts Difference of Two Squares Pattern Algebra Example = ( + )( ) x 9 = x 3 = ( x + 3)( x 3) a b a b a b Notes: Perfect Square Trinomial Pattern Algebra Example + + = ( + ) x x x ( x)( ) a ab b a b = ( x 3) = + + = ( ) x x x ( x)( ) a ab b a b Notes: = ( x 3) = 36 Algebra 1 Copyright Big Ideas Learning, LLC

35 7.7 Notetaking with Vocabulary (continued) Extra Practice In Exercises 1 6, factor the polynomial. 1. s 49. t x 4. 4g h k In Exercises 7 1, use a special product pattern to evaluate the expression

36 Name Date 7.7 Notetaking with Vocabulary (continued) In Exercises 13 18, factor the polynomial. 13. x + 16x p + 8p r 6r a 18a c + 84c x 0x + 1 In Exercises 19 4, solve the equation. 19. x 144 = y = c + 14c + 49 = 0. d 4d + 4 = 0 3. n + n = k + 9 = k The dimensions of a rectangular prism are ( x + 1) feet by ( ) prism is ( 4x 1) cubic feet. What is the value of x? x + feet by 4 feet. The volume of the 38 Algebra 1 Copyright Big Ideas Learning, LLC

37 7.8 Factoring Polynomials Completely For use with Exploration 7.8 Essential Question How can you factor a polynomial completely? 1 EXPLORATION: Writing a Product of Linear Factors Work with a partner. Write the product represented by the algebra tiles. Then multiply to write the polynomial in standard form. a. ( )( )( ) b. ( )( )( ) c. ( )( )( ) d. ( )( )( ) e. ( )( )( ) f. ( )( )( ) EXPLORATION: Matching Standard and Factored Forms Work with a partner. Match the standard form of the polynomial with the equivalent factored form on the next page. Explain your strategy. x a. 3 d. 3 + x b. x 4x + 4x e. 3 x x c. 3 x x 3x f. 3 x + x x 3 x x + x g. x x h. 3 4 x + x i. 3 x x 3 j. 3 x 3x x + k. 3 x x 3x + l. 3 x 4x + 3x m. x x n. 3 3 x 4x 4x + + o. 3 x + x + x 39

38 Name Date 7.8 Factoring Polynomials Completely (continued) EXPLORATION: Matching Standard and Factored Forms (continued) A. xx ( + 1)( x 1) B. xx ( 1) C. xx+ ( 1) D. xx ( + )( x 1) E. xx ( 1)( x ) F. xx ( + )( x ) G. xx ( ) H. xx+ ( ) I. x ( x 1) J. x ( x + 1) K. x ( x ) L. x ( x + ) M. xx ( + 3)( x 1) N. xx ( + 1)( x 3) O. xx ( 1)( x 3) Communicate Your Answer 3. How can you factor a polynomial completely? 4. Use your answer to Question 3 to factor each polynomial completely. 3 3 x + 4x + 3x b. x 6x + 9x c. x + 6x + 9x a Algebra 1 Copyright Big Ideas Learning, LLC

39 7.8 Notetaking with Vocabulary For use after Lesson 7.8 In your own words, write the meaning of each vocabulary term. factoring by grouping factored completely Core Concepts Factoring by Grouping To factor a polynomial with four terms, group the terms into pairs. Factor the GCF out of each pair of terms. Look for and factor out the common binomial factor. This process is called factoring by grouping. Notes: Guidelines for Factoring Polynomials Completely To factor a polynomial completely, you should try each of these steps. 1. Factor out the greatest common monomial factor. 3x + 6x = 3x( x + ). Look for a difference of two squares or a perfect square trinomial. x + 4 x + 4 = ( x + ) 3. Factor a trinomial of the form ax + bx + c into a product 3x 5x = 3x + 1 x of binomial factors. ( )( ) 4. Factor a polynomial with four terms by grouping. x 3 + x 4x 4 = ( x + 1)( x 4) Notes: 41

40 Name Date 7.8 Notetaking with Vocabulary (continued) Extra Practice In Exercises 1 8, factor the polynomial by grouping. b 4b + b 4. ac + ad + bc + bd d + c + cd + d 4. 5t + 6t + 5t s + s 64s a + a 30a x 1x 5x h + 18h 35h Algebra 1 Copyright Big Ideas Learning, LLC

41 7.8 Notetaking with Vocabulary (continued) In Exercises 9 16, factor the polynomial completely c 4c x 5x 11. a + 3a 1. 9x + 3x p p x 0x s + s 1s t + t 10t 5 In Exercises 17, solve the equation x 1x + 30 = y 5y = 19. c 81c = d + 9 = d + d 1. 48n 3n = 0. x + 3x = 16x

### 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

### 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

### Maintaining Mathematical Proficiency

Chapter Maintaining Mathematical Proficiency Simplify the expression. 1. 8x 9x 2. 25r 5 7r r + 3. 3 ( 3x 5) + + x. 3y ( 2y 5) + 11 5. 3( h 7) 7( 10 h) 2 2 +. 5 8x + 5x + 8x Find the volume or surface area

### Essential Question How can you factor a polynomial completely?

REASONING ABSTRACTLY 7.8 To be proficient in math, ou need to know and flexibl use different properties of operations and objects. Factoring Polnomials Completel Essential Question How can ou factor a

### 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

### 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

### 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

### UNIT 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

### 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

### 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

### 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

### Find two positive factors of 24 whose sum is 10. Make an organized list.

9.5 Study Guide For use with pages 582 589 GOAL Factor trinomials of the form x 2 1 bx 1 c. EXAMPLE 1 Factor when b and c are positive Factor x 2 1 10x 1 24. Find two positive factors of 24 whose sum is

### 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

### 8-1: Adding and Subtracting Polynomials

8-1: Adding and Subtracting Polynomials Objective: To classify, add, and subtract polynomials Warm Up: Simplify each expression. 1. x 3 7 x 9. 6(3x 4) 3. 7 ( x 8) 4 4. 5(4x (8x 6) monomial - A real number,

### 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 +

### Chapter 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,

### 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.

### 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

### MathB65 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

### = 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

### 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.

### 7.7. 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

### 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

### 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

### SECTION 1.4 PolyNomiAls feet. Figure 1. A = s 2 = (2x) 2 = 4x 2 A = 2 (2x) 3 _ 2 = 1 _ = 3 _. A = lw = x 1. = x

SECTION 1.4 PolyNomiAls 4 1 learning ObjeCTIveS In this section, you will: Identify the degree and leading coefficient of polynomials. Add and subtract polynomials. Multiply polynomials. Use FOIL to multiply

### MathB65 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

### Math 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

### Quick-and-Easy Factoring. of lower degree; several processes are available to fi nd factors.

Lesson 11-3 Quick-and-Easy Factoring BIG IDEA Some polynomials can be factored into polynomials of lower degree; several processes are available to fi nd factors. Vocabulary factoring a polynomial factored

### 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

### 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

### 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:

### 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:

### Mathwithsheppard.weebly.com

Unit #: Powers and Polynomials Unit Outline: Date Lesson Title Assignment Completed.1 Introduction to Algebra. Discovering the Exponent Laws Part 1. Discovering the Exponent Laws Part. Multiplying and

### 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

### Using the Laws of Exponents to Simplify Rational Exponents

6. Explain Radicals and Rational Exponents - Notes Main Ideas/ Questions Essential Question: How do you simplify expressions with rational exponents? Notes/Examples What You Will Learn Evaluate and simplify

### 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

### Multiplication 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

### Unit 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

### = 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives:

Math 65 / Notes & Practice #1 / 20 points / Due. / Name: Home Work Practice: Simplify the following expressions by reducing the fractions: 16 = 4 = 8xy =? = 9 40 32 38x 64 16 Solve the following equations

Algebra I Book 2 Powered by... ALGEBRA I Units 4-7 by The Algebra I Development Team ALGEBRA I UNIT 4 POWERS AND POLYNOMIALS......... 1 4.0 Review................ 2 4.1 Properties of Exponents..........

### 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

### Factoring Polynomials. Review and extend factoring skills. LEARN ABOUT the Math. Mai claims that, for any natural number n, the function

Factoring Polynomials GOAL Review and extend factoring skills. LEARN ABOUT the Math Mai claims that, for any natural number n, the function f (n) 5 n 3 1 3n 2 1 2n 1 6 always generates values that are

### 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

### Algebra 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

### Math 10 - Unit 5 Final Review - Polynomials

Class: Date: Math 10 - Unit 5 Final Review - Polynomials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Factor the binomial 44a + 99a 2. a. a(44 + 99a)

### 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

### 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 +

### Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term")... so it says "many terms

Polynomials Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term")... so it says "many terms Polynomials A polynomial looks like this: Term A number, a variable, or the

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 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

### SEE the Big Idea. of a Falling Object (p. 400) Game Reserve (p. 394) Photo Cropping (p. 390) Gateway Arch (p. 382) Framing a Photo (p.

7 Polynomial Equations and Factoring 7.1 Adding and Subtracting Polynomials 7.2 Multiplying Polynomials 7.3 Special Products of Polynomials 7.4 Solving Polynomial Equations in Factored Form 7.5 Factoring

### 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

### 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

### Section 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

### 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

### The 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

### 7-4. } 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

### 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

### 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

### Mini-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

### 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

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

### ACTIVITY: 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.

### 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

### 9.4 Start Thinking. 9.4 Warm Up. 9.4 Cumulative Review Warm Up. Use a graphing calculator to graph ( )

9.4 Start Thinking Use a graphing calculator to graph ( ) f x = x + 4x 1. Find the minimum of the function using the CALC feature on the graphing calculator. Explain the relationship between the minimum

### 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

### Lecture 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 &

### 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

### 9-1 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

### 5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014. c = Properites of Exponents. *Simplify each of the following:

48 5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014 Properites of Exponents 1. x a x b = x a+b *Simplify each of the following: a. x 4 x 8 = b. x 5 x 7 x = 2. xa xb = xa b c. 5 6 5 11 = d. x14

### 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,

### 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

### 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

### Section 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,

### Unit 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

### Secondary 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

### NAME DATE PERIOD. Study Guide and Intervention. Solving Polynomial Equations. For any number of terms, check for: greatest common factor

5-5 Factor Polynomials Study Guide and Intervention For any number of terms, check for: greatest common factor Techniques for Factoring Polynomials For two terms, check for: Difference of two squares a

### MAFS Algebra 1. Polynomials. Day 15 - Student Packet

MAFS Algebra 1 Polynomials Day 15 - Student Packet Day 15: Polynomials MAFS.91.A-SSE.1., MAFS.91.A-SSE..3a,b, MAFS.91.A-APR..3, MAFS.91.F-IF.3.7c I CAN rewrite algebraic expressions in different equivalent

### 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

### 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

### Using Properties of Exponents

6.1 Using Properties of Exponents Goals p Use properties of exponents to evaluate and simplify expressions involving powers. p Use exponents and scientific notation to solve real-life problems. VOCABULARY

### Review Unit Multiple Choice Identify the choice that best completes the statement or answers the question.

Review Unit 3 1201 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following numbers is not both a perfect square and a perfect cube? a. 531

### 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

### Get 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.

### 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

### 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

### 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

Adding and Subtracting Polynomials Polynomial A monomial or sum of monomials. Binomials and Trinomial are also polynomials. Binomials are sum of two monomials Trinomials are sum of three monomials Degree

### LESSON 6.3 POLYNOMIAL OPERATIONS II

LESSON 6.3 POLYNOMIAL OPERATIONS II LESSON 6.3 POLYNOMIALS OPERATIONS II 277 OVERVIEW Here's what you'll learn in this lesson: Multiplying Binomials a. Multiplying binomials by the FOIL method b. Perfect

### Prerequisites. Introduction CHAPTER OUTLINE

Prerequisites 1 Figure 1 Credit: Andreas Kambanls CHAPTER OUTLINE 1.1 Real Numbers: Algebra Essentials 1.2 Exponents and Scientific Notation 1.3 Radicals and Rational Expressions 1.4 Polynomials 1.5 Factoring

### Factoring Polynomials Using the GCF

7.6 Factoring Polynomials Using the GCF polynomial in factored form? How can you use common factors to write a 1 ACTIVITY: Finding Monomial Factors Work with a partner. Six different algebra tiles are

### Algebra 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

### 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

### Day 7: Polynomials MAFS.912.A-SSE.1.2, MAFS.912.A-SSE.2.3a,b, MAFS.912.A-APR.2.3, MAFS.912.F-IF.3.7c

Day 7: Polynomials MAFS.91.A-SSE.1., MAFS.91.A-SSE..3a,b, MAFS.91.A-APR..3, MAFS.91.F-IF.3.7c I CAN rewrite algebraic expressions in different equivalent forms using factoring techniques use equivalent

### Chapter Six. Polynomials. Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring

Chapter Six Polynomials Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring Properties of Exponents The properties below form the basis