algebra 1 unit 8 part 1 note sheets...

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

1

Date Name of Lesson Notes

9.1 Adding and Subtracting Polynomials Pack

9.2 Multiplying Polynomials Pack

9.3 Find Special Products of Polynomials Pack

Factoring By Greatest Common Factor By

Hand

Factoring By GCF and Solving Pack

Factor By Grouping #1 Pack

Factor By Grouping #2 By

Hand

9.5 Factoring 𝑎𝑥2 + 𝑏𝑥 + 𝑐 Part 1 Pack

9.6 Factoring 𝑎𝑥2 + 𝑏𝑥 + 𝑐 Part 2 Pack

9.6 Solving 𝑎𝑥2 + 𝑏𝑥 + 𝑐 Pack

Factoring Activity TBD

9.7 Factor Special Products Pack

Review

Review

Test

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

2

9.1 Adding and Subtracting Polynomials Date:

Objective:

Polynomial –

Monomial –

Binomial –

Leading Coefficient -

Degree of Polynomial –

Degree of Monomial –

Trinomial –

Like Terms -

Guided Practice

1. Write 15x – x3 + 3 so that the exponents decrease from left to right. Identify the degree and leading

coefficient of the polynomial.

Tell whether the expression is a polynomial. If it is a polynomial, find its degree and classify it by the number

of its terms. Otherwise, tell why it is not a polynomial.

Expression Is it a Polynomial? Classify by degree and number of

terms

9

2x2 + x – 5

6n4 – 8n

n– 2 – 3

7bc3 + 4b4c

Your Turn

2. Write 5y – 2y2 + 9 so that the exponents decrease from left to right. Identify the degree and leading

coefficient of the polynomial.

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

3

3. Tell whether y3 – 4y + 3 is a polynomial. If it is a polynomial, find its degree and classify it by the number of

its terms. Otherwise, tell why it is not a polynomial.

Guided Practice

Simplify each expression

4. 2x +3x 5. -4m + 6m + (-8m)

6. (2x3 – 5x2 + x) + (2x2 + x3 – 1) 7. (3x2 + x – 6) + (x2 + 4x + 10)

Your Turn

8. (5x3 + 4x – 2x) + (4x2 +3x3 – 6)

Guided Practice

9. (4n2 + 5) – (–2n2 + 2n – 4) 10. (4x2 – 3x + 5) – (3x2 – x – 8)

Your Turn

9. (4x2 – 7x) – (5x2 + 4x – 9)

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

4

9.2 Multiplying Polynomials Notes Date:

WARM UP:

OBJECTIVE:

Guided Practice

1. Find the product 2x3(x3 + 3x2 – 2x + 5). 2. Find the product (x – 4)(3x + 2).

Your Turn

3. 𝑥(7𝑥2 + 4) 4. (𝑎 + 3)(2𝑎 + 1) 5. (4𝑛 – 1)(𝑛 + 5)

Guided Practice

6. (𝑏2 + 6𝑏 − 7)(3𝑏 + 4) 7. (2𝑥2 + 5𝑥 – 1)(4𝑥 – 3)

FOIL

(2𝑥 + 3)(4𝑥 + 1)

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

5

Guided Practice

8. (3𝑎 + 4)(𝑎 – 2)

Your Turn

9. (𝑥2 + 2𝑥 + 1)(𝑥 + 2) 10. (3𝑦2 – 𝑦 + 5)(2𝑦 – 3)

11. (4𝑏 – 5)(𝑏 – 2)

Guided Practice

12. The dimensions of a rectangle are x + 3 and x + 2. Which expression represents the area of the

rectangle?

Your Turn

13. The dimensions of a rectangle are x + 5 and x + 9. Which expression represents the area of the

rectangle?

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

6

9.3 Special Products of Polynomials Notes Date:

WARM UP Find the product

1. (x + 7) (x + 2) 2. (3x – 1) (3x + 2) 3. (b2 – 2b – 1) (3b – 5)

OBJECTIVE:

Square of a Binomial Pattern

Guided Practice

1. (3x + 4)2 2. (5x – 2y)2

Your Turn

3. (x + 3)2 4. (2x + 1)2

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

7

5. (4x – y)2 6. (3m + n)2

Sum and Difference Pattern

Guided Practice

7. (t + 5)(t – 5) 8. (3x + y)(3x – y)

Your Turn

9. (x + 10)(x – 10) 10. (2x + 1)(2x – 1)

11. (x + 3y)(x – 3y)

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

8

Factoring By GCF and Solving Date:

WARM UP

Solve each equation

1. . Factor 4𝑥2 + 2𝑥 2. If 2x=0 then x=

Objective:

Zero Product Property:

What are the Zeros of an equation/function?_______________________________________________

Guided Practice

1. Solve 2𝑥2 + 8𝑥 = 0.

2. Solve 6𝑛2 = 15𝑛.

Your Turn

3. 𝑎2 + 5𝑎 = 0 4. 3𝑠2 – 9𝑠 = 0

5. 4𝑥2 = 2𝑥

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

9

9.8 Factor by Grouping Date: Warm-Up: Factor out the greatest common monomial factor.

1. 2.

Guided Practice

1. Factor 3xy – 21y + 5x – 35

2. Factor 8𝑚2𝑛 − 5𝑚 − 24𝑚𝑛 + 15

Your Turn

3. 15𝑥 − 3𝑥𝑦 − 20 + 4𝑦

4. 6𝑎𝑏 + 4𝑏 − 21𝑎 − 14

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

10

5. 4𝑥 + 6𝑝𝑎 − 8𝑎 − 3𝑝𝑥 Hint rearrange the terms!!!

Guided Practice

6. 6𝑥3 − 9𝑥2 + 4𝑥 − 6

Your Turn

7. 8𝑥3 + 2𝑥2 + 12𝑥 + 3

8. 4𝑥3 − 6𝑥2 − 6𝑥 + 9

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

11

9.5 Factor 𝒙𝟐 + 𝒃𝒙 + 𝒄 Date: Warm-up Solve by factoring

1. What two numbers multiply to 10 and add to 7? a.

2. What two numbers multiply to 10 and add to 11? a.

3. What to numbers multiply to 8 and add to 9? a.

4. What two numbers multiply to 8 and add to -6? a.

Objective:

Guided Practice Factor.

1. x2 + 11x + 10 2. x2 + 3x + 2

3. x2 + 9x + 14

Your Turn

4. 𝑥2 + 5𝑥 + 6 5. 𝑥2 + 11𝑥 + 28

Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________

Period:______

12

6. 𝑥2 + 9𝑥 + 18 Guided Practice

7. x2 - 6x + 8

8. 15x2 + 7x - 2

9. x2 + 2x - 15

Your Turn

10. 𝑥2 − 8𝑥 + 12

11. 𝑥2 + 6𝑥 −

Algebra 1 Unit 8 Part 2 Note Sheets

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9.6 Factor 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 Part 1 Date: Warm up:

1. What multiplies to -30 and adds to -13?

a.

2. What multiplies to -30 and adds to -17?

a.

Objective: Guided Practice

5. Factor 3x2 -13x -10

6. 2x2 - 5x - 7

7. 15x2 + 7x - 2

Algebra 1 Unit 8 Part 2 Note Sheets

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Your Turn 8. 3x2 + 11x – 20 9. 5𝑦2 + 13𝑦 − 6

10. 2𝑧2 + 9𝑧 − 5

Algebra 1 Unit 8 Part 2 Note Sheets

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9.6 Factor 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 Part 2 Date: Warm-up

Use the x-box method to factor the following.

1.−𝒙𝟐 + 𝟏𝟐𝒙 − 𝟐𝟕 2. 𝟔𝒚𝟐 − 𝟓𝒚 − 𝟒

Objective:

Recall: Zero Product Property _______________________________________________________________________ The zeros of an equation/functions____________________________________________________ Guided Practice Solve the equation.

1. 2𝑥2 − 3𝑥 − 35 = 0

2. 4𝑥2 + 11𝑥 − 3 = 0

Your Turn

3. 2𝑥2 + 𝑥 − 15 = 0 4. 3𝑦2 + 22𝑦 + 7 = 0

Algebra 1 Unit 8 Part 2 Note Sheets

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5. 4𝑧2 − 2𝑥 − 90 = 0

Guided Practice Find the zeros of the polynomial function.

6. 𝑓(𝑥) = 3𝑥2 + 𝑥 − 14

Your Turn

7. 𝑓(𝑥) = 2𝑥2 + 𝑥 − 1

Algebra 1 Unit 8 Part 2 Note Sheets

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9.7 Factor Special Products Date: Warm up

1. Factor 𝟒𝒙𝟐 − 𝟑𝒙 − 𝟕 2. Find the zeros: 𝟐𝒚𝟐 − 𝟓𝒚 = 𝟑𝟑 Objective: Guided Practice

1. x2 - 12x + 36

Perfect Square Trinomial Pattern

2. 9𝑥2 − 12𝑥 + 4

Your Turn

3. 𝑥2 + 4𝑥 + 4 4. 4𝑥2 − 36𝑥 + 81

Guided Practice

5. 2𝑥2 − 20𝑥 + 50

6. 3𝑥2 + 6𝑥𝑦 + 3𝑦2

Algebra 1 Unit 8 Part 2 Note Sheets

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Your Turn

7. 3𝑦2 − 36𝑦 + 108 8. 4𝑥2 + 4𝑥𝑦 + 𝑦2

Difference of Two Squares Pattern

Guided Practice 9. y2 – 16 10. 25m2 – 36 11. x2 – 49y2

Your Turn

12. 𝑥2 − 64 13. 4𝑥2 − 400

Algebra 1 Unit 8 Part 2 Note Sheets

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Factoring Word Problems Date: Warm-up Factor.

1. 𝒙𝟐 − 𝟔𝒙 − 𝟏𝟔 2. 𝒙𝟐 + 𝒙 − 𝟏𝟐 3. 𝟔𝒙𝟐 − 𝟏𝟑𝒙 − 𝟓

Guided Practice

1. The square of a number equals nine times that number. Find the number

2. The area of a square is equal to five times its perimeter. Find the length of the side of the square.

Your Turn

3. Suppose that four times the square of a number equals twenty times that number. What is the number?

4. The area of a square is equal to twice its perimeter. Find the length of the side of the square.

Guided Practice

5. The combined area of two squares is 20 square centimeters. Each side of one square is twice as long as

the side of the other square. Find the lengths of the sides of each square.

Your Turn

6. The combined area of two squares is 250 square feet. Each side of one square is three times as long as

the side of the other square. Find the lengths of the sides of each square.

Algebra 1 Unit 8 Part 2 Note Sheets

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Guided Practice

7. Find two consecutive integers whose product is 72.

Your Turn

7. Find two consecutive integers whose product is 110.

Guided Practice

9. A rectangular plot is 6 meters longer than it is wide. The area of the plot is 16 square meters. Find the

length and width of the plot.

Your Turn

10. A rectangular plot is 2 yards longer than it is wide. The area of the plot is 80 square yards. Find the

width and length of the plot.

Guided Practice

11. The area of a triangular sheet of paper is 14 square inches. One side of the triangle is 3 inches longer

than the altitude to that side. Find the length of the one side and the length of the altitude to that side.

Your Turn

12. The area of a triangular piece of glass is 30 square inches. One side of the triangle is 4 inches longer

than the altitude to that side. Find the length of that side and the length of the altitude to that side.