algebra 1 unit 8 part 1 note sheets...
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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 ππ₯2 + ππ₯ + π Part 1 Pack
9.6 Factoring ππ₯2 + ππ₯ + π Part 2 Pack
9.6 Solving ππ₯2 + ππ₯ + π 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 β
Monomial β
Binomial β
Leading Coefficient -
Degree of Polynomial β
Degree of Monomial β
Trinomial β
Like Terms -
Guided Practice
1. Write 15x β 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 β 5
6n4 β 8n
nβ 2 β 3
7bc3 + 4b4c
Your Turn
2. Write 5y β 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 β 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 β 5x2 + x) + (2x2 + x3 β 1) 7. (3x2 + x β 6) + (x2 + 4x + 10)
Your Turn
8. (5x3 + 4x β 2x) + (4x2 +3x3 β 6)
Guided Practice
9. (4n2 + 5) β (β2n2 + 2n β 4) 10. (4x2 β 3x + 5) β (3x2 β x β 8)
Your Turn
9. (4x2 β 7x) β (5x2 + 4x β 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 β 2x + 5). 2. Find the product (x β 4)(3x + 2).
Your Turn
3. π₯(7π₯2 + 4) 4. (π + 3)(2π + 1) 5. (4π β 1)(π + 5)
Guided Practice
6. (π2 + 6π β 7)(3π + 4) 7. (2π₯2 + 5π₯ β 1)(4π₯ β 3)
FOIL
(2π₯ + 3)(4π₯ + 1)
Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________
Period:______
5
Guided Practice
8. (3π + 4)(π β 2)
Your Turn
9. (π₯2 + 2π₯ + 1)(π₯ + 2) 10. (3π¦2 β π¦ + 5)(2π¦ β 3)
11. (4π β 5)(π β 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 β 1) (3x + 2) 3. (b2 β 2b β 1) (3b β 5)
OBJECTIVE:
Square of a Binomial Pattern
Guided Practice
1. (3x + 4)2 2. (5x β 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 β y)2 6. (3m + n)2
Sum and Difference Pattern
Guided Practice
7. (t + 5)(t β 5) 8. (3x + y)(3x β y)
Your Turn
9. (x + 10)(x β 10) 10. (2x + 1)(2x β 1)
11. (x + 3y)(x β 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 4π₯2 + 2π₯ 2. If 2x=0 then x=
Objective:
Zero Product Property:
What are the Zeros of an equation/function?_______________________________________________
Guided Practice
1. Solve 2π₯2 + 8π₯ = 0.
2. Solve 6π2 = 15π.
Your Turn
3. π2 + 5π = 0 4. 3π 2 β 9π = 0
5. 4π₯2 = 2π₯
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 β 21y + 5x β 35
2. Factor 8π2π β 5π β 24ππ + 15
Your Turn
3. 15π₯ β 3π₯π¦ β 20 + 4π¦
4. 6ππ + 4π β 21π β 14
Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________
Period:______
10
5. 4π₯ + 6ππ β 8π β 3ππ₯ Hint rearrange the terms!!!
Guided Practice
6. 6π₯3 β 9π₯2 + 4π₯ β 6
Your Turn
7. 8π₯3 + 2π₯2 + 12π₯ + 3
8. 4π₯3 β 6π₯2 β 6π₯ + 9
Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________
Period:______
11
9.5 Factor ππ + ππ + π 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. π₯2 + 5π₯ + 6 5. π₯2 + 11π₯ + 28
Algebra 1 Unit 8 Part 1 Note Sheets Name:_________________________
Period:______
12
6. π₯2 + 9π₯ + 18 Guided Practice
7. x2 - 6x + 8
8. 15x2 + 7x - 2
9. x2 + 2x - 15
Your Turn
10. π₯2 β 8π₯ + 12
11. π₯2 + 6π₯ β
Algebra 1 Unit 8 Part 2 Note Sheets
13
9.6 Factor πππ + ππ + π 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
14
Your Turn 8. 3x2 + 11x β 20 9. 5π¦2 + 13π¦ β 6
10. 2π§2 + 9π§ β 5
Algebra 1 Unit 8 Part 2 Note Sheets
15
9.6 Factor πππ + ππ + π Part 2 Date: Warm-up
Use the x-box method to factor the following.
1.βππ + πππ β ππ 2. πππ β ππ β π
Objective:
Recall: Zero Product Property _______________________________________________________________________ The zeros of an equation/functions____________________________________________________ Guided Practice Solve the equation.
1. 2π₯2 β 3π₯ β 35 = 0
2. 4π₯2 + 11π₯ β 3 = 0
Your Turn
3. 2π₯2 + π₯ β 15 = 0 4. 3π¦2 + 22π¦ + 7 = 0
Algebra 1 Unit 8 Part 2 Note Sheets
16
5. 4π§2 β 2π₯ β 90 = 0
Guided Practice Find the zeros of the polynomial function.
6. π(π₯) = 3π₯2 + π₯ β 14
Your Turn
7. π(π₯) = 2π₯2 + π₯ β 1
Algebra 1 Unit 8 Part 2 Note Sheets
17
9.7 Factor Special Products Date: Warm up
1. Factor πππ β ππ β π 2. Find the zeros: πππ β ππ = ππ Objective: Guided Practice
1. x2 - 12x + 36
Perfect Square Trinomial Pattern
2. 9π₯2 β 12π₯ + 4
Your Turn
3. π₯2 + 4π₯ + 4 4. 4π₯2 β 36π₯ + 81
Guided Practice
5. 2π₯2 β 20π₯ + 50
6. 3π₯2 + 6π₯π¦ + 3π¦2
Algebra 1 Unit 8 Part 2 Note Sheets
18
Your Turn
7. 3π¦2 β 36π¦ + 108 8. 4π₯2 + 4π₯π¦ + π¦2
Difference of Two Squares Pattern
Guided Practice 9. y2 β 16 10. 25m2 β 36 11. x2 β 49y2
Your Turn
12. π₯2 β 64 13. 4π₯2 β 400
Algebra 1 Unit 8 Part 2 Note Sheets
19
Factoring Word Problems Date: Warm-up Factor.
1. ππ β ππ β ππ 2. ππ + π β ππ 3. πππ β πππ β π
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
20
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.