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 our practice, have I attempt all practice I attempt all homework I never give up when I don t understand #INTEGRITY as we help others with their work, maintain a #GO-FOR-IT attitude, continually I always check my answers I correct my work, I never just copy answers I explain answers, I never just give them I write down all notes, even if I m confused I remain positive about my goals I treat each day as a chance to reset #ENCOURAGE each other to succeed as a team, and always #REACH-OUT and ask for help when we need it! I offer help when I understand the material I push my teammates to reach their goals I never let my teammates give up I ask my questions during homework check I ask my teammates for help during practice I attend enrichment/tutorials when I need to Unit 8 Polynomials 2
Unit Calendar MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY February 9 10 11 12 13 Polynomial Vocabulary Add and Subtract Polynomials Multiplying Polynomials 16 17 18 19 20 Multiplying Multiplying Polynomials Polynomials Holiday QUIZ Early Release 23 24 25 26 27 Factor GCF Factor GCF Factor Factor QUIZ March 2 3 4 5 6 Factor Factor Review Review TEST Essential Question How can I use what I know about operations with real numbers to help me with operations with algebraic expressions? Unit 8 Polynomials 3
Critical Vocabulary Polynomial Term Degree Factor Unit 8 Polynomials 4
Polynomials: Basics and Vocabulary Term A combination of, and. Like Term Terms that have the same and combination. Polynomial A combination of one or more terms named by their and number of. Degree Name: Degree Example Name 0 1 2 3 4 or more Number of Terms Name: Terms Example Name 1 2 3 4 or more Unit 8 Polynomials 5
Examples: Classify each polynomial by its degree and nuber of terms: 2 6x 5x 2 15 3 4g 2g Combine like terms and arrange in descending order: 2x 2 + 5x + 6 3x 2 2 2 2 a 2b 4a 2 8a 2b 7a 4a 2 Practice: Classify each polynomial by its degree and nuber of terms: c 6 2 2a 5a 1 2 9x 5x 6 2 4 3 x x 2x x 3x 3 2 5n 10n 4n 3 2 3 3x x 4x 2 10x 1 Combine like terms and arrange in descending order: 2 4x 1 3x 5 2x 3xy 5 2xy 10 4x + 10x 7x 2 y + 3x 2 2y 2 + 7x 2 5x 2 y 12r + 5 + 3r 5 x 2 + 4x 3x 5x + 3x + 7 x 4 x 2 3x + 4 + 3x 2 x 2 + 5x 3 6x 2x 2 Unit 8 Polynomials 6
Unit 8 Polynomials 7
Polynomials: Adding and Subtracting Use algebra tiles to find the sum. (x 2 x + 1) + (6x 3) (3x 2 + 2x + 5) + ( x 2 x 4) + + Examples: (6x 2 + 3x) + (2x 2 + 6x) ( 6x 3 + 5x) + (4x 3 + x 2 2x + 9) (ab 2 + 13b 4a) + (3ab 2 + a 2 b + a + 7b (11hz 3 + 8hz) (9hz 3 3hz z) Find the perimeter of a rectangle with length 4x + 3 and width 2x 1. The perimeter of a triangle is 6x 2 + 5x + 9. If two of the sides are 3x 2 + x + 2 and x 2 + 2x + 1, find the missing side. Unit 8 Polynomials 8
Practice: (2y 2 + 3y) + (y 2 + 7y) (9x 3 5x) (3x) (2x 3 + 4x 2) (4x 3 6) ( 5y 2 + 7y 2) + (4y 2 + y + 8) (4x 3 + x 2 ) + (2x 3 3) (t 3 2t) (t 2 2t + 6) (12d 2 + 3dx + x) ( 4d 2 + 2dx 8x) (4x 3 y x 2 + 4x) + (x 3 y x 2 4x) Find the perimeter of a triangle with side lengths 2x 2 + 3x 1, 5x + 2, and 3x 2 + 5. The perimeter of a rectangle is 10x + 6. If the width is 2x + 1, what is the length? 2x + 1 2x + 1 Unit 8 Polynomials 9
Unit 8 Polynomials 10
Polynomials: Multiplying Use algebra tiles to find the product. 4(x 3) (2x)(3x) (x + 1)(x 2) Examples: 5x(x 3) 4x(x 2 + 8) (x + 4)(x 5) (3n + 2)(6n + 1) Unit 8 Polynomials 11
Practice: 3x(x + 8) 2x( 2x 4 3) 8y(x 3y) (x 2)(x + 8) (x 3)(x 6) (x 7)(x + 7) (2x + 1)(x + 2) (x + 3)(x 4) (3x 4)(2x 5) Unit 7 Multiplication Practice: (3x)(x 2 y 3 ) (2ab)(5a 3 b) Unit 8 Polynomials 12
Polynomials: Multiplying Cont Examples: ( 5b 3 )( 2b + 1 ) (3 4x)(8 + 3x) (-2x + 7y)(3x 5y) (2x 5)(4x 2-3x + 1) Unit 8 Polynomials 13
Practice: (2x 1)(x + 3) ( 4n + 3 )( 3n - 2 ) (x 3)(x 2 +3x+2) (2 + 5z)(3 4z) (3m + 2)(5m 6) ( x - 7)( x² + 7x 4 ) (-6a +5b)(5a 4b) (2y - 3)(6y 7) (3x + 2)(2x 2-5x - 7) Unit 8 Polynomials 14
Polynomials: Multiplying Cont Examples: (5x + 2)(5x 2) (4x 3) 2 (y 1)(y + 2) + 2x(x + 2) x(2x 6) (x + 3)(2x + 3) A sidewalk was built around a rectangular swimming pool. Which expression below describes the area of the sidewalk? 2x+5 3x+3 3x x+4 Unit 8 Polynomials 15
Practice: (x + 4)(x 4) (4m 9) 2 2g(g 5) + (g + 2)(3g 1) (5z + 2)(z 9) (z 5) Find the area of the shaded portion. 12x+2 2x 5x-2 3x+5 (x + 8)(x 8) (y 6) 2 Unit 8 Polynomials 16
Unit 8 Polynomials 17
Factoring: Greatest Common Factor Distributive Property a(b + c) = ab + ac Factoring a GCF ab + ac = a(b + c) Think: Un - What is the number all the coefficients can divide by? That s the constant you can Factor out. Do ALL the terms have a common variable? o If so, what is the exponent of that variable? That s how many you can Factor out. Examples: x 2 + 3x 15y 3 + 20y 5 10 8s 4 t + 20t 3 28t 2 20ac 2 + 15a 2 c 5ac Unit 8 Polynomials 18
Practice: x 2 + 2x 5m 3 + 45 10x 2 2x 20x 2 y 2 4xy 5m 4 n 5m 3 n + 5m 2 b 2 8b 8c 2 + 7c 44a 2 + 11a 12t 5 + 6t 9x 2 + 6x + 18 Unit 8 Polynomials 19
Factoring: Greatest Common Factor Cont Examples: The area of a rectangle is 4x 2 + 10x and the width is 2x. Find the measure of the length. x(z 5) + 4(z 5) 3x(2x+1) 1(2x+1) Practice: 15-5a 2 10g 3-3g 15x 4-5x 2 8y(d 2) + 3(d 2) x(z + 10) + 7(z + 10) x(x - 4) + 3(x - 4) 2r(r 1) + 3(r 1) -20ab 3 c 4 d 5ab 2 c 2 3x 3 y - 6x 2 y 2-3xy 3 The area of a garden is 14x 2 y 2 z + 21xy 2 z 2. The length is 7xy 2 z. What is the width? Unit 8 Polynomials 20
Unit 8 Polynomials 21
Fatoring: Trinomials Examples: x 2 2 + 8x + 15 5x 17x 6 x 2 + 13x + 36 3x 2 + 14x + 8 Unit 8 Polynomials 22
Practice: x 2 2 + 8x + 7 4x 16x 15 2 6x 19x 10 x 2 + 16x + 64 x 2 + 7x + 6 2x 2 + 11x + 14 n 2 2 + 6n + 9 3x 17x 20 n 2 + 11n + 10 x 2 + 26x + 48 Unit 8 Polynomials 23
Fatoring: Trinomials Cont Examples: x 2 + 2x 3 2x 2 6x + 4 a 2 2 13a 30 4x 9x 9 Unit 8 Polynomials 24
Practice: x 2 2 11x + 30 3x x 4 2 4x 12x 7 x 2 8x + 12 m 2 2 + m 90 5x 7x 6 7x 2-5x 2 n 2 + 4n 12 Unit 8 Polynomials 25
Fatoring: Special Answers Examples: x 2 9 4x 2 25 4x 2 + 20x + 25 6x 2 7x 3 Unit 8 Polynomials 26
Practice: x 2 100 9x 2 4 9x 2 12x + 4 4x 2 + 4x - 15 x 2 + 10x + 25 9y 2 121 6x 2 13x 15 8x 2 2x 1 Unit 8 Polynomials 27
Fatoring: Trinomials with Greatest Common Factors Sometimes you have to factor out a GCF and then continue factoring: 6x 2 + 6x 36 6(x 2 + x 6) (x + 3)(x 2) Factoring Review: 3x 2 2 + 15x + 18 3x 8x 5 4x 2 16 4x 2 4x + 168 Unit 8 Polynomials 28
Practice: 3x 2 2 + 9x 120 4x 4x 1 5x 2 2 50x + 45 16x 1 2 3x 8x 4 2 2x 18 2 3x 12x 12 4x 2 + 10x 6 Unit 8 Polynomials 29
Unit 8 Polynomials 30
Unit 8 Polynomials 31