STUDY GUIDE
GRADE 8 | UNIT 1
Factoring
Table of Contents
Introduction ......................................................................................................................................... 3
Test Your Prerequisite Skills ............................................................................................................. 4
Objectives............................................................................................................................................ 5
Lesson 1: Factoring Polynomials with a Common Monomial Factor
- Warm Up! ................................................................................................................................. 5
- Learn about It! ........................................................................................................................ 6
- Let’s Practice! .......................................................................................................................... 7
- Check Your Understanding! ................................................................................................ 12
Lesson 2: Factoring the Difference of Two Squares
- Warm Up! ............................................................................................................................... 13
- Learn about It! ...................................................................................................................... 15
- Let’s Practice! ........................................................................................................................ 17
- Check Your Understanding! ................................................................................................ 22
Lesson 3: Factoring the Sum or Difference of Two Cubes
- Warm Up! ............................................................................................................................... 23
- Learn about It! ...................................................................................................................... 24
- Let’s Practice! ........................................................................................................................ 25
- Check Your Understanding! ................................................................................................ 30
Lesson 4: Factoring Perfect Square Trinomials
- Warm Up! ............................................................................................................................... 31
- Learn about It! ...................................................................................................................... 32
- Let’s Practice! ........................................................................................................................ 34
- Check Your Understanding! ................................................................................................ 39
1
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Lesson 5: Factoring General Trinomials
- Warm Up! ............................................................................................................................... 40
- Learn about It! ...................................................................................................................... 41
- Let’s Practice! ........................................................................................................................ 42
- Check Your Understanding! ................................................................................................ 49
Challenge Yourself! .......................................................................................................................... 49
Performance Task ............................................................................................................................ 50
Wrap-up............................................................................................................................................. 54
Key to Let’s Practice! ......................................................................................................................... 55
References ........................................................................................................................................ 56
2
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, STUDY GUIDE
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Table of Contents
GRADE 8 | MATHEMATICS
UNIT 1
Factoring
Mathematics relies on logic and creativity, and it is studied both for its theoretical and
practical applications. For some people, not just the
professionals, the pursuit to understand the essence of
mathematics lies in the study of patterns and relationships.
For grade 8 students, the pursuit to study mathematics starts
with the understanding of the concepts of polynomials.
For some, it is not outright clear when or where the application of the study polynomials
can be readily applied. However, even the simplest tasks or scenarios can be modeled
using polynomials.
Have you ever wondered how architects maximize and design a
certain floor plan of a house or a building? …or how an engineer
computes for the right mixture of cement and gravel to be used for
the foundations of skyscrapers and other infrastructures? …or simply
how a carpenter builds a cabinet or drawer using limited supplies?
In this unit, you will learn about the different factoring techniques that
will be useful in simplifying polynomials as well as their applications in the real world.
3
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, STUDY GUIDE
Test Your Prerequisite Skills
Computing the area and volume of two- and three-dimensional figures
Performing basic operations on polynomials
Finding special products
Before you get started, answer the following items to help you assess your prior
knowledge and practice some skills that you will need in studying the lessons in this unit.
1. List all the positive integer factors of the given number.
a. 9 b. 16 c. 51
2. Perform the indicated operation.
a.
b.
c.
d.
e.
f.
3. Expand the following expressions using special product formulas.
a. c.
b. d.
4. Give the formulas for the following:
a. area of a rectangle
b. area of a square
c. area of a triangle
d. area of a circle
e. volume of a cube
f. volume of a rectangular prism
4
Copyright © 2018 Quipper Limited
GRADE 8 | UNIT 1
Factoring
Table of Contents
Introduction ......................................................................................................................................... 3
Test Your Prerequisite Skills ............................................................................................................. 4
Objectives............................................................................................................................................ 5
Lesson 1: Factoring Polynomials with a Common Monomial Factor
- Warm Up! ................................................................................................................................. 5
- Learn about It! ........................................................................................................................ 6
- Let’s Practice! .......................................................................................................................... 7
- Check Your Understanding! ................................................................................................ 12
Lesson 2: Factoring the Difference of Two Squares
- Warm Up! ............................................................................................................................... 13
- Learn about It! ...................................................................................................................... 15
- Let’s Practice! ........................................................................................................................ 17
- Check Your Understanding! ................................................................................................ 22
Lesson 3: Factoring the Sum or Difference of Two Cubes
- Warm Up! ............................................................................................................................... 23
- Learn about It! ...................................................................................................................... 24
- Let’s Practice! ........................................................................................................................ 25
- Check Your Understanding! ................................................................................................ 30
Lesson 4: Factoring Perfect Square Trinomials
- Warm Up! ............................................................................................................................... 31
- Learn about It! ...................................................................................................................... 32
- Let’s Practice! ........................................................................................................................ 34
- Check Your Understanding! ................................................................................................ 39
1
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, STUDY GUIDE
Lesson 5: Factoring General Trinomials
- Warm Up! ............................................................................................................................... 40
- Learn about It! ...................................................................................................................... 41
- Let’s Practice! ........................................................................................................................ 42
- Check Your Understanding! ................................................................................................ 49
Challenge Yourself! .......................................................................................................................... 49
Performance Task ............................................................................................................................ 50
Wrap-up............................................................................................................................................. 54
Key to Let’s Practice! ......................................................................................................................... 55
References ........................................................................................................................................ 56
2
Copyright © 2018 Quipper Limited
, STUDY GUIDE
Click Home icon to go back to
Table of Contents
GRADE 8 | MATHEMATICS
UNIT 1
Factoring
Mathematics relies on logic and creativity, and it is studied both for its theoretical and
practical applications. For some people, not just the
professionals, the pursuit to understand the essence of
mathematics lies in the study of patterns and relationships.
For grade 8 students, the pursuit to study mathematics starts
with the understanding of the concepts of polynomials.
For some, it is not outright clear when or where the application of the study polynomials
can be readily applied. However, even the simplest tasks or scenarios can be modeled
using polynomials.
Have you ever wondered how architects maximize and design a
certain floor plan of a house or a building? …or how an engineer
computes for the right mixture of cement and gravel to be used for
the foundations of skyscrapers and other infrastructures? …or simply
how a carpenter builds a cabinet or drawer using limited supplies?
In this unit, you will learn about the different factoring techniques that
will be useful in simplifying polynomials as well as their applications in the real world.
3
Copyright © 2018 Quipper Limited
, STUDY GUIDE
Test Your Prerequisite Skills
Computing the area and volume of two- and three-dimensional figures
Performing basic operations on polynomials
Finding special products
Before you get started, answer the following items to help you assess your prior
knowledge and practice some skills that you will need in studying the lessons in this unit.
1. List all the positive integer factors of the given number.
a. 9 b. 16 c. 51
2. Perform the indicated operation.
a.
b.
c.
d.
e.
f.
3. Expand the following expressions using special product formulas.
a. c.
b. d.
4. Give the formulas for the following:
a. area of a rectangle
b. area of a square
c. area of a triangle
d. area of a circle
e. volume of a cube
f. volume of a rectangular prism
4
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