Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 8 8 - Complete.… ·  · 2015-02-17I always check my answers I correct my work, ... Polynomials 3 Unit

Unit 8 – Polynomials 1

Name: ____________________ Teacher: _____________ Per: ___

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Unit 8

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Unit 10

– Unit 8 – [Polynomials]

Unit 8 – Polynomials 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…

I always check my answers I correct my work, I never just copy answers I explain answers, I never just give them

#GO-FOR-IT attitude, continually…

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…

I offer help when I understand the material I push my teammates to reach their goals I never let my teammates give up

#REACH-OUT and ask for help when we need it!

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 3

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

Holiday

Multiplying Polynomials

QUIZ

Multiplying Polynomials

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 4

Critical Vocabulary

Polynomial

Term

Degree

Factor

Unit 8 – Polynomials 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

0

1

2

3

4 or more

Number of Terms Name:

Terms Example Name

1

2

3

4 or more

Unit 8 – Polynomials 6

Examples:

Classify each polynomial by its degree and nuber of terms:

26 5 2x x

15 34 2g g

Combine like terms and arrange in descending order:

2𝑥2 + 5𝑥 + 6 − 3𝑥2

2 2 2a 2b 4a 2 8a 2b 7a 4a 2

Practice:

Classify each polynomial by its degree and nuber of terms:

6c

22 5 1a a 29 5x x

6

2 4 32x x x x 3x

3 25 10 4n n n

3 23 3 4x x x 210 1x

Combine like terms and arrange in descending order:

24x 1 3x 5 2x

3xy 5 2xy 10 −4𝑥 + 10𝑥

7𝑥2𝑦 + 3𝑥2 − 2𝑦2 + 7𝑥2 − 5𝑥2𝑦

12𝑟 + 5 + 3𝑟 − 5 𝑥2 + 4𝑥 − 3𝑥

5𝑥 + 3𝑥 + 7 − 𝑥 − 4

𝑥2 − 3𝑥 + 4 + 3x – 2 𝑥2 + 5𝑥 − 3 − 6𝑥 − 2𝑥2

Unit 8 – Polynomials 7

Unit 8 – Polynomials 8

Polynomials: Adding and Subtracting

Use algebra tiles to find the sum. (𝑥2 − 𝑥 + 1) + (6𝑥 − 3) (3𝑥2 + 2𝑥 + 5) + (−𝑥2 − 𝑥 − 4)

Examples:

(6𝑥2 + 3𝑥) + (2𝑥2 + 6𝑥)

(−6𝑥3 + 5𝑥) + (4𝑥3 + 𝑥2 − 2𝑥 + 9)

(𝑎𝑏2 + 13𝑏 − 4𝑎) + (3𝑎𝑏2 + 𝑎2𝑏 + 𝑎 + 7𝑏

(11ℎ𝑧3 + 8ℎ𝑧) − (9ℎ𝑧3 − 3ℎ𝑧 − 𝑧)

Find the perimeter of a rectangle with length 4x + 3 and width 2x – 1.

The perimeter of a triangle is 6x2 + 5x + 9. If two of the sides are 3x2 + x + 2 and x2 + 2x + 1, find the missing side.

+ +

Unit 8 – Polynomials 9

Practice:

(2𝑦2 + 3𝑦) + (𝑦2 + 7𝑦)

(9𝑥3 − 5𝑥) − (3𝑥)

(2𝑥3 + 4𝑥 − 2) − (4𝑥3 − 6)

(−5𝑦2 + 7𝑦 − 2) + (4𝑦2 + 𝑦 + 8)

(4𝑥3 + 𝑥2) + (2𝑥3 − 3)

(𝑡3 − 2𝑡) − (𝑡2 − 2𝑡 + 6)

(12𝑑2 + 3𝑑𝑥 + 𝑥) − (−4𝑑2 + 2𝑑𝑥 − 8𝑥)

(4𝑥3𝑦 − 𝑥2 + 4𝑥) + (𝑥3𝑦 − 𝑥2 − 4𝑥)

Find the perimeter of a triangle with side lengths 2x2 + 3x – 1, 5x + 2, and 3x2 + 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 10

Unit 8 – Polynomials 11

Polynomials: Multiplying

Use algebra tiles to find the product.

4(𝑥 − 3) (2𝑥)(3𝑥) (𝑥 + 1)(𝑥 − 2)

Examples:

5𝑥(𝑥 − 3)

−4𝑥(𝑥2 + 8) (𝑥 + 4)(𝑥 − 5) (3𝑛 + 2)(6𝑛 + 1)

Unit 8 – Polynomials 12

Practice:

3𝑥(𝑥 + 8)

2𝑥(−2𝑥4 − 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)(𝑥2𝑦3)

(2𝑎𝑏)(5𝑎3𝑏)

Unit 8 – Polynomials 13

Polynomials: Multiplying Cont…

Examples:

( 5b – 3 )( 2b + 1 )

(3 – 4x)(8 + 3x)

(-2x + 7y)(3x – 5y)

(2x – 5)(4x2 - 3x + 1)

Unit 8 – Polynomials 14

Practice:

(2x – 1)(x + 3)

( 4n + 3 )( 3n - 2 ) (x – 3)(x2+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)(2x2 - 5x - 7)

Unit 8 – Polynomials 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 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.

(𝑥 + 8)(𝑥 − 8)

(𝑦 − 6)2

2x

3x+5

12x+2

5x-2

Unit 8 – Polynomials 17

Unit 8 – Polynomials 18

Factoring: Greatest Common Factor

Distributive Property Factoring a GCF

𝑎(𝑏 + 𝑐) = 𝑎𝑏 + 𝑎𝑐 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:

𝑥2 + 3𝑥

15𝑦3 + 20𝑦5 − 10

−8𝑠4𝑡 + 20𝑡3 − 28𝑡2

20𝑎𝑐2 + 15𝑎2𝑐 − 5𝑎𝑐

Unit 8 – Polynomials 19

Practice:

𝑥2 + 2𝑥

5𝑚3 + 45

10𝑥2 − 2𝑥

20𝑥2𝑦2 − 4𝑥𝑦

−5𝑚4𝑛 − 5𝑚3𝑛 + 5𝑚2

𝑏2 − 8𝑏

8𝑐2 + 7𝑐

44𝑎2 + 11𝑎

−12𝑡5 + 6𝑡

9𝑥2 + 6𝑥 + 18

Unit 8 – Polynomials 20

Factoring: Greatest Common Factor Cont…

Examples:

The area of a rectangle is 4x2 + 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 - 5a2

10g3 - 3g 15x4 - 5x2

8y(d – 2) + 3(d – 2)

x(z + 10) + 7(z + 10) x(x - 4) + 3(x - 4)

2r(r – 1) + 3(r – 1)

-20ab3c4d – 5ab2c2 3x3y - 6x2y2 - 3xy3

The area of a garden is 14x2y2z + 21xy2z2. The length is 7xy2z. What is the width?

Unit 8 – Polynomials 21

Unit 8 – Polynomials 22

Fatoring: Trinomials

Examples:

𝑥2 + 8𝑥 + 15

25 17 6x x

𝑥2 + 13𝑥 + 36

3x2 + 14x + 8

Unit 8 – Polynomials 23

Practice:

𝑥2 + 8𝑥 + 7

24 16 15x x

26 19 10x x

𝑥2 + 16𝑥 + 64

𝑥2 + 7𝑥 + 6

2x2 + 11x + 14

𝑛2 + 6𝑛 + 9

23 17 20x x

𝑛2 + 11𝑛 + 10

𝑥2 + 26𝑥 + 48

Unit 8 – Polynomials 24

Fatoring: Trinomials Cont…

Examples:

𝑥2 + 2𝑥 − 3

2x2 – 6x + 4

𝑎2 − 13𝑎 − 30

24 9 9x x

Unit 8 – Polynomials 25

Practice:

𝑥2 − 11𝑥 + 30

23 4x x

24 12 7x x

𝑥2 − 8𝑥 + 12

𝑚2 + 𝑚 − 90

25 7 6x x

7x2 - 5x – 2

𝑛2 + 4𝑛 − 12

Unit 8 – Polynomials 26

Fatoring: Special Answers

Examples:

x2 − 9

4𝑥2 − 25

4𝑥2 + 20𝑥 + 25

6x2 – 7x – 3

Unit 8 – Polynomials 27

Practice:

𝑥2 − 100

9𝑥2 − 4

9𝑥2 − 12𝑥 + 4

4x2 + 4x - 15

𝑥2 + 10𝑥 + 25

9𝑦2 − 121

6x2 – 13x – 15

8x2 – 2x – 1

Unit 8 – Polynomials 28

Fatoring: Trinomials with Greatest Common Factors

Sometimes you have to factor out a GCF and then continue factoring:

6𝑥2 + 6𝑥 − 36

6(𝑥2 + 𝑥 − 6)

(𝑥 + 3)(𝑥 − 2)

Factoring Review:

3𝑥2 + 15𝑥 + 18

23 8 5x x

4x2 – 16

4𝑥2 − 4𝑥 + 168

Unit 8 – Polynomials 29

Practice:

3𝑥2 + 9𝑥 − 120

24 4 1x x

5𝑥2 − 50𝑥 + 45

216 1x

23 8 4x x

22 18x

23 12 12x x

4x2 + 10x – 6

Unit 8 – Polynomials 30

Unit 8 – Polynomials 31