This document provides a detailed lesson plan for an 8th grade mathematics class on factoring polynomials with common monomial factors. The lesson plan outlines objectives, content, learning resources, procedures, evaluation, and reflection. Key points of the lesson include identifying the greatest common factor of terms, using it to factor polynomials by dividing each term, and applying factoring to solve real-world problems like finding the width of a rectangular garden. Student activities involve practicing identifying common factors, completing factoring problems, and generalizing the factoring process. The teacher evaluates student learning through a multiple choice assessment.

1. GRADE
8
DETAILED
LESSON PLAN
School RIO TUBA NATIONAL HIGH
SCHOOL
Grade Level 8
Teacher Catherine S. Partidas Learning
Area
Mathematics 8
Teaching
Dates and
Time
October 19,2023
7:30-8:30
Quarter FIRST
I. OBJECTIVES
A. Content Standard The learners demonstrate understanding of key concepts of factors of polynomials
B. Performance
Standard
The learners formulate real-life problems involving factors and solve these with utmost
accuracy using a variety of strategies.
C. Learning
Competency/
Objectives
Learning Competency: Factors completely different types of polynomials
(polynomials with common monomial factor, difference of two squares, sum and
difference of two cubes, perfect square trinomials, and general trinomials).
M8AL-Ia-b-1
Learning Objectives:
1. Identify the common monomial factor of the given polynomials.
2. Factor polynomial with common monomial factor.
3. Appreciates the importance of factoring in real-life situation.
D. Peace Education Harmony with Others
Willingness to share with others
II. CONTENT Factoring polynomials with greatest common monomial factor
III. LEARNING
RESOURCES
A. References Mathematics Learner’s Module 8
1. Teacher’s Guide
pages
2. Learner’s Material
pages
pages 29-31
3. Textbooks pages
4. Additional
Materials from
Learning Resources
Rubelyn Joy E. Saclausa, Lou Welah B. Ducena, Mathematics Grade 8, Alternative
Delivery Mode,
Quarter 1 – Module 1: Factoring Polynomials First Edition, 2020. DepEd Region XII,
Regional Administrative Center, Brgy Carpenter Hill,Koronadal City, South Cotabato.
B. Other Learning
Resources
IV. PROCEDURES TEACHER’S ACTIVITY STUDENTS’ACTIVITY
A. Before the lesson
Elicit
A. Reviewing
previous
lesson or
presenting
Classroom Routine (Prayer, Greetings,
Energizer, Checking of Attendance,
Reminders)
Let us start by reviewing the concept of
factor and factors.
Are you ready?
Students do the classroom routine.

2. the new
lesson
What is factor?
What are the factors of 5?
What are the factors of 9?
How about the factor of 11?
Since you already how to find the factors of
a number. Let’s go ahead to the next
activity.
Factor is a number or algebraic
expression that divides another number
or expression evenly, that is with no
remainder.
Student’s answer is 1 and 5.
Student’s answer is 1,3,9.
Student’s answer is 1 and 11.
Engage
B. Establishing a
purpose for
the lesson.
The teacher let the students observe the
pictures of icons.
1. Who are the people in these photos?
2. What do they have in common?
3. What are the things that make them
different from each other?
What about the common in the expression
2𝑥2
+ 4𝑥 ?
Before we discuss our lesson for today,
everyone please read the objectives of our
lesson.
In this lesson you are expected to learned:
1. Identify the common monomial factor of
the given polynomials.
2. Factor polynomial with common
monomial factor.
3. Appreciates the importance of factoring
in real-life situation.
1. Darna, Jose Rizal and
Superman
2. They are all heroes.
3. Student’s answer may vary.

3. Explore
C. Presenting
examples/
instances of the
new lesson
Let the student identify the common in the
following.
Identify the common in the following.
1. 2, 4, 6
2. 3, 6, 9
3. 2x, 3x, 5x
4. 2a, 2b ,2c
5. 𝟐𝒙𝟐
𝒚, 𝟒𝒙𝒚 , 𝟖𝒙𝒚
Common factors are factors that two or
more numbers have in common.
The Greatest Common Factor (GCF) is
refer to the common factor having the
greatest
numerical factor and with variables having
the least degree.
Factoring is the process of finding the
factors of an expression which is the
reversed process of multiplication.
Common monomial factoring is the process
of writing a polynomial as a product of two
polynomials ,one which is a monomial that
factor each term of the polynomial.
Note: Use the Greatest Common Factor of
the terms of the given polynomial.
1. They are divisible by 2.
2. They are divisible by 3.
3. They have common variable x.
4. They have common numerical
coefficient .
5. They have common variable x,
and can be divided by 2.
Explain
D. Discussing new
concepts and
practicing new
skills # 1
Let the student answer the following:
1. Find the GCF of 4x and 10?
2. Find the GCF of 4𝑚2
𝑎𝑛𝑑 10𝑚.
3. Find the GCF of
6𝑥4
, 9𝑥2
𝑦, 𝑎𝑛𝑑 15𝑥5
𝑦
Now ,you are ready to find the greatest
common factor of a given polynomials with
common monomial factor.
Observe and analyze the steps:
Step 1 : Find the greatest common factor
(GCF) of the terms in the polynomial. This is
the first factor.
Step 2: Divide each term by the GCF to get
the other factor.
Students can use techniques and
finding the GCF of an expressions.
1. 2
2. 2m
3. 3𝑥2
𝑦

4. E. Discussing new
concepts and
practicing new skills #
2
Complete the table to practice this type of
factoring.
Polynomi
al
Greatest
Common
Factor
(CMF)
Quotient
of
Polynomi
al and
CMF
Factored
Form
2𝑥2
+ 4𝑥
6𝑥 − 2
𝟓𝒙𝟐
𝐲 + 𝟏𝟎𝒙𝟐
𝒚
+ 𝟐𝟓𝒙𝟐
𝒚
Factor 1. 2𝑥2
+ 4𝑥
Step 1 : Find the greatest common factor
(GCF) of the terms in the polynomial. This is
the first factor.
2𝑥2
= 2. 𝑥. 𝑥
4𝑥 = 2.2. 𝑥
GCMF: 2.x = 2x
Step 2: Divide each term by the GCF to get
the other factor.
2𝑥2
2𝑥
+
4𝑥
2𝑥
𝑥 + 2
Factor 6𝑥 − 2
Step 1 : Find the greatest common factor
(GCF) of the terms in the polynomial. This is
the first factor.
6𝑥 = 2.3. 𝑥
2=2.1
GCMF: 2
Step 2 : Divide each term by the GCF to
get the other factor.
6𝑥
2
-
2
2
3𝑥 − 1
Let the student answer number 3.
Factor 3. 𝟓𝒙𝟐
𝐲 + 𝟏𝟎𝒙𝟑
𝒚 + 𝟐𝟓𝒙𝟒
𝒚
Step 1 : Find the greatest common
factor (GCF) of the terms in the
polynomial. This is the first factor.
𝟓𝒙𝟐
𝐲 = 𝟏. 𝟓. 𝐱. 𝐱. 𝐲
𝟏𝟎𝒙𝟑
𝒚 = 𝟓. 𝟐. 𝒙. 𝒙. 𝒙. 𝒚
𝟐𝟓𝒙𝟒𝒚 = 𝟓. 𝟓. 𝒙. 𝒙. 𝒙. 𝒙. 𝒚
GCMF: 5.x.x=𝟓𝒙𝟐𝒚
Step 2: Divide each term by the GCF to
get the other factor.
𝟓𝒙𝟐
𝐲
𝟓𝒙𝟐
𝒚
+
𝟏𝟎𝒙𝟑
𝒚
𝟓𝒙𝟐
𝒚
+
𝟐𝟓𝒙𝟒
𝒚
𝟓𝒙𝟐
𝒚
1 + 2𝑥 + 𝟓𝒙𝟐

5. F. Developing
mastery (leads to
formative assessment
3)
The teacher lets the students complete
the table.
Elaborate
G. Finding practical
applications of
concepts and skills in
daily living.
Teacher will discuss how factoring applied
in real-life situation.
Example:
Rio Tuba National High School has a
rectangular garden with an area of 4𝑥4
+
6𝑥3
+ 8𝑥. If the length of the rectangular
garden is 2x, what is the width of the
garden.
Let the students answer.
Answer:
2𝑥3
+ 3𝑥2
+ 4
H. Making
generalization and
abstractions about
the lesson.
The teacher summarizes the lesson through
questions like:
1. How can you identify the common
monomial factor of a given
polynomial?
2. What are the steps in finding the
factors of a polynomial the common
monomial factor?
3. What is the importance of factoring
polynomials in real life situation?
Students answer may vary.

6. Evaluation
I. Evaluating Learning
Choose the letter that corresponds
to the of the correct answer.
1. What is the GCF of
𝑎3
𝑏3
𝑎𝑛𝑑 𝑎2
𝑏5
?
a. 𝑎2
𝑏3
b. 𝑎2
𝑏5
c. 𝑎3
𝑏3
d. 𝑎3
𝑏5
2. The GCF of 14𝑥7
𝑎𝑛𝑑 10𝑥4
is ___________.
a. 2x
b. 2𝑥4
c. 2𝑥7
d. 10𝑥4
3. Factor 2𝑓2
− 6𝑓3
.
a. 2𝑓2(𝑓 − 3𝑓2)
b. 2𝑓2(1 − 3𝑓)
c. 2𝑓3(8 − 6𝑓2)
d. 3𝑓(1 − 3𝑓)
4. The factored form of
56𝑎3
− 8𝑎 𝑖𝑠 _______________.
a. 8𝑎(7𝑎3
− 𝑎)
b. 8𝑎2(35𝑎2
− 𝑎)
c. 8𝑎(7𝑎2
− 1)
d. 8𝑎2(56𝑎3
− 8𝑎)
5. Factor the polynomial
16𝑥9
𝑦9
− 24𝑥6
𝑦7
− 16𝑥3
𝑦2
.
a. 8𝑥3(2𝑥3
𝑦9
− 3𝑥3
𝑦7
−
2𝑦2)
b. 𝑁𝑜 𝑐𝑜𝑚𝑚𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟
c. 8𝑥3
𝑦2(2𝑥6
𝑦7
− 3𝑥3
𝑦5
−
2)
d. 8(2𝑥9
𝑦9
− 3𝑥6
𝑦7
−
2𝑥3
𝑦2)
Answer:
1. A 2. B 3. B 4.C 5. C
Extend
J. Additional activities
or remediation
Create three expressions in the trinomial
form that can be completely factored with
their respected factored forms.

7. Prepared by:
Catherine S. Partidas
Teacher I
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned 80% in
the evaluation
B. No. of learners
who require additional
activities for
remediation who
scored below 80%
C. Did the remedial
lessons work? No. of
learners who have
caught up with the
lesson.
D. No. of learners
who continue to
require remediation.
E. Which of my
teaching strategies
worked well? Why did
this work?
F. What difficulties did
I encounter which my
principal or supervisor
can help me solve?
G. What innovation or
localization materials
did I use/discover
which to share with
other teachers?