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math 10 plus
chapter 3
Ms. Albarico
Nanchang No. 2 High School
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TABLE OF CONTENTS 3.1 Factors and Multiples of Whole
Number3.2 Perfect Squares, Perfect Cubes, and Their Roots3.3 Common Factors of a Polynomial3.4 Math Lab: Modelling Trinomials as Binomial Products3.5 Polynomials of the Form x2+ bx + c3.6 Polynomials of the Form ax2+ bx + c3.7 Multiplying Polynomials3.8 Factoring Special Polynomials
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3.1 & 3.2 Curriculum Outcome
Students will be expected to demonstrate an understanding of
factors of whole numbers by determining the prime factors, greatest common factor, least
common multiple, square root, and cube root.
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3.1 & 3.2 Specific Outcomes
Determine the prime factors of a whole number. Explain why the numbers 0 and 1 have no prime factors. Determine, using a variety of strategies, the greatest
common factor or least common multiple of a set of whole numbers, and explain the process.
Determine, concretely, whether a given whole number is a perfect square, a perfect cube, or neither.
Determine, using a variety of strategies, the square root of a perfect square, and explain the process.
Determine, using a variety of strategies, the cube root of a perfect cube, and explain the process.
Solve problems that involve prime factors, greatest common factors, least common multiples, square roots, or cube roots.
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Lesson 3.1
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PRIME FACTORIZATION
The prime factorization of a
natural number is the number
written as a product of itsprime factors.
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Prime Factorization Quiz Online Prime Factorization Lecture
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Example 1
Determining the Prime Factors of a Whole Number
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Determining the Prime Factors of a Whole Number
Example 1
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GREATEST COMMON FACTOR
The greatest commonfactor of two or more
numbers is the greatestfactor the numbers have in
common.
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Greatest Common Factor Quiz Online
Greatest Common Factor Activity
Greatest Common Factor Module
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Determining the Greatest Common Factor
Example 2
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Determining the Greatest Common Factor
Example 2
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Determining the Greatest Common Factor
Example 2
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LEAST COMMON MULTIPLE
The least common multiple of two or more
numbers is the least number that is divisible by each
number.
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Least Common Multiple Game HG
Least Common Multiple Module
Least Common Multiple Game SB
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Determining the Least Common Multiple
Example 3
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Determining the Least Common Multiple
Example 3
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Solving Problems that Involve Greatest Common Factorand Least Common Multiple
Example 4
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Solving Problems that Involve Greatest Common Factorand Least Common Multiple
Example 4
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Solving Problems that Involve Greatest Common Factorand Least Common Multiple
Example 4
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Solving Problems that Involve Greatest Common Factorand Least Common Multiple
Example 4
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Solving Problems that Involve Greatest Common Factorand Least Common Multiple
Example 4
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PRACTICE EXERCISES
Answer # 3-11(classwork)13-22 (homework) on
pages 140-141.
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Lesson 3.2
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Key Terms
Index - Radicand - Radical -
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Key Terms
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PERFECT SQUARE
Any whole number that can be represented as the area of a square with a whole number side length is a perfect square.
The side length of the square is the square root of the area of the square.
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PERFECT SQUARE
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Calculator Command
SQUARE ROOT
Press 2nd then x2
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Example 1
Determining the Square Root of a Whole Number
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Example 1
Determining the Square Root of a Whole Number
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PERFECT CUBE
Any whole number that can be represented as the volume of a cube with a whole number edge length is a perfect cube.
The edge length of the cube is the cube root of the volume of the cube.
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PERFECT CUBE
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Calculator Command
CUBE ROOT
Press math then choose #4
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Example 2
Determining the Cube Root of a Whole Number
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Example 2
Determining the Cube Root of a Whole Number
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Example3
Using Roots to Solve a Problem
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Practice Exercises
Answer # 4-18 on pages 146-147.
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Practice Exercises
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Checkpoint!
Draw the diagram in your notebook on page 148.
Homework!
Answer ASSESS YOUR UNDERTSANDING questions 1-10 in your notebook on page 149.
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EXTRA LESSON – CUBE ROOT
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Objective: You will be able to determine if a number is a perfect cube and to find the
cube root of a number that is a perfect cube.
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Remember
A cube is a three dimensional prism with 6 square faces; so all sides are congruent and all angles are right angles.
Perfect Cubes and Cube Roots
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Squares and Cubes:Similarities- All sides congruent- All angles 90 degrees
Differences:- Square is 2 dimensional- Cube is 3 dimensional that number’s
square root.
Perfect Cubes and Cube Roots
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Remember
A number is a perfect square if you can take that many 1 x 1 unit squares and form them into a square. The side length of the square you form is that number’s square root.
Perfect Cubes and Cube Roots
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A number is a perfect cube if you can take that many 1 x 1 x 1 unit cubes and form them into a cube. The side length of the cube you form is that number’s cube root.is that number’s square root.
Perfect Cubes and Cube Roots
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Is 8 a perfect cube?that number’s square root.
Perfect Cubes and Cube Roots
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that.
Perfect Cubes and Cube Roots
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that.
Perfect Cubes and Cube Roots
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8 is a perfect cube and its cube root is 2
Perfect Cubes and Cube Roots
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Is 5 a perfect cube?
Perfect Cubes and Cube Roots
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Is 5 a perfect cube?
Perfect Cubes and Cube Roots
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Three Dimensions
Perfect Cube
Volume
Perfect Cubes and Cube Roots
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Perfect Cube: 8 Cube Root 2
Volume: 8 units3 Side Length: 2 units
Perfect Cubes and Cube Roots
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Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
2 units
2 x 2 x 2 8 units3 8
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Perfect Cube: Cube Root
Volume: units3 Side Length: units
Perfect Cubes and Cube Roots
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Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 1 x 1 x 1 1 units3 1
2 units
2 x 2 x 2 8 units3 8
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Perfect Cube: Cube Root
Volume: units3 Side Length: units
Perfect Cubes and Cube Roots
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Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 13 1 units3 1
2 units
23 8 units3 8
3 units
33 27 units3 27
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Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 13 1 units3 1
2 units
23 8 units3 8
3 units
33 27 units3 27
4 units
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Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 13 1 units3 1
2 units
23 8 units3 8
3 units
33 27 units3 27
4 units
43
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Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 13 1 units3 1
2 units
23 8 units3 8
3 units
33 27 units3 27
4 units
43 64 units3
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Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 13 1 units3 1
2 units
23 8 units3 8
3 units
33 27 units3 27
4 units
43 64 units3 64
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Perfect Cubes and Cube Roots
Side Length
Volume Operation
Volume Perfect Cube
1 unit 13 1 units3 1
2 units
23 8 units3 8
3 units
33 27 units3 27
4 units
43 64 units3 64
S units
S3 S3 units3 S3
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Perfect Cubes and Cube Roots
Side Length of cube
Volume Operation
Volume of cube
Perfect Cube
1 unit 13 1 units3 1
2 units 23 8 units3 8
3 units 33 27 units3
27
4 units 43 64 units3
64
S units S3 S3 units3 S3
10 units
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Perfect Cubes and Cube Roots
Side Length of cube
Volume Operation
Volume of cube
Perfect Cube
1 unit 13 1 units3 1
2 units 23 8 units3 8
3 units 33 27 units3
27
4 units 43 64 units3
64
S units S3 S3 units3 S3
10 units
103
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Perfect Cubes and Cube Roots
Side Length of cube
Volume Operation
Volume of cube
Perfect Cube
1 unit 13 1 units3 1
2 units 23 8 units3 8
3 units 33 27 units3
27
4 units 43 64 units3
64
S units S3 S3 units3 S3
10 units
103 1000 u3
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Perfect Cubes and Cube Roots
Side Length of cube
Volume Operation
Volume of cube
Perfect Cube
1 unit 13 1 units3 1
2 units 23 8 units3 8
3 units 33 27 units3
27
4 units 43 64 units3
64
S units S3 S3 units3 S3
10 units
103 1000 u3 1000
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Square Root
Perfect Cubes and Cube Roots
![Page 73: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649dd25503460f94ac8f7d/html5/thumbnails/73.jpg)
Square Root Cube Root
Perfect Cubes and Cube Roots
![Page 74: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649dd25503460f94ac8f7d/html5/thumbnails/74.jpg)
Square Root Cube Root
Perfect Cubes and Cube Roots
![Page 75: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649dd25503460f94ac8f7d/html5/thumbnails/75.jpg)
Square Root Cube Root
Perfect Cubes and Cube Roots
![Page 76: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649dd25503460f94ac8f7d/html5/thumbnails/76.jpg)
Practice
Perfect Cubes and Cube Roots
![Page 77: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649dd25503460f94ac8f7d/html5/thumbnails/77.jpg)
Practice
Is 827 a perfect cube?
Perfect Cubes and Cube Roots
![Page 78: Students will be expected to demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649dd25503460f94ac8f7d/html5/thumbnails/78.jpg)
Conclusion: You can now determine if a number is a perfect cube and find the cube
root of a number that is a perfect cube.