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
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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
2 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
3 Unit Calendar MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY February Polynomial Vocabulary Add and Subtract Polynomials Multiplying Polynomials Multiplying Multiplying Polynomials Polynomials Holiday QUIZ Early Release Factor GCF Factor GCF Factor Factor QUIZ March 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
4 Critical Vocabulary Polynomial Term Degree Factor Unit 8 Polynomials 4
5 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 or more Number of Terms Name: Terms Example Name or more Unit 8 Polynomials 5
6 Examples: Classify each polynomial by its degree and nuber of terms: 2 6x 5x g 2g Combine like terms and arrange in descending order: 2x 2 + 5x + 6 3x 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 x x 2x x 3x 3 2 5n 10n 4n x 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 r 5 x 2 + 4x 3x 5x + 3x + 7 x 4 x 2 3x x 2 x 2 + 5x 3 6x 2x 2 Unit 8 Polynomials 6
7 Unit 8 Polynomials 7
8 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 b 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
9 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 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
10 Unit 8 Polynomials 10
11 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
12 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
13 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
14 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
15 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
16 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
17 Unit 8 Polynomials 17
18 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 y s 4 t + 20t 3 28t 2 20ac a 2 c 5ac Unit 8 Polynomials 18
19 Practice: x 2 + 2x 5m x 2 2x 20x 2 y 2 4xy 5m 4 n 5m 3 n + 5m 2 b 2 8b 8c 2 + 7c 44a a 12t 5 + 6t 9x 2 + 6x + 18 Unit 8 Polynomials 19
20 Factoring: Greatest Common Factor Cont Examples: The area of a rectangle is 4x x 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
21 Unit 8 Polynomials 21
22 Fatoring: Trinomials Examples: x x x 17x 6 x x x x + 8 Unit 8 Polynomials 22
23 Practice: x x + 7 4x 16x x 19x 10 x x + 64 x 2 + 7x + 6 2x x + 14 n n + 9 3x 17x 20 n n + 10 x x + 48 Unit 8 Polynomials 23
24 Fatoring: Trinomials Cont Examples: x 2 + 2x 3 2x 2 6x + 4 a a 30 4x 9x 9 Unit 8 Polynomials 24
25 Practice: x x x x 4 2 4x 12x 7 x 2 8x + 12 m m 90 5x 7x 6 7x 2-5x 2 n 2 + 4n 12 Unit 8 Polynomials 25
26 Fatoring: Special Answers Examples: x 2 9 4x x x x 2 7x 3 Unit 8 Polynomials 26
27 Practice: x x 2 4 9x 2 12x + 4 4x 2 + 4x - 15 x x y x 2 13x 15 8x 2 2x 1 Unit 8 Polynomials 27
28 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 x x 8x 5 4x x 2 4x Unit 8 Polynomials 28
29 Practice: 3x x 120 4x 4x 1 5x x x 1 2 3x 8x 4 2 2x x 12x 12 4x x 6 Unit 8 Polynomials 29
30 Unit 8 Polynomials 30
31 Unit 8 Polynomials 31
Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10. Unit 9a. [Quadratic Functions] Unit 9 Quadratics 1
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Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 9a [Quadratic Functions] Unit 9 Quadratics 1 To be a Successful Algebra class, TIGERs will show #TENACITY
Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10. Unit 4. [Writing Linear Equations]
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Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 4 [Writing Linear Equations] Find the equation of a line that has slope m = 4 and passes through the point
Unit 3a. [Graphing Linear Equations] Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10
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Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 3a [Graphing Linear Equations] Unit 2 Solving Equations 1 To be a Successful Algebra class, TIGERs will show
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