1. The document outlines a daily lesson log for an 8th grade mathematics class covering factoring polynomials. 2. The lesson objectives are to factor different types of polynomials including those with a common monomial factor, the difference of two squares, the sum and difference of two cubes, and perfect square trinomials. 3. The lesson procedures include reviewing factors, presenting examples of each type of factoring, having students practice problems, and making generalizations about factoring polynomials.

1. GRADE 8
DAILY LESSON LOG
School Grade Level 8
Teacher Learning Area MATHEMATICS
Teaching Dates and Time Quarter FIRST
Session 1 Session 2 Session 3 Session 4
I. OBJECTIVES
1. Content Standards The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions,
linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and
linear functions.
2. Performance
Standards
The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions,
linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and
linear functions, and solve these problems accurately using a variety of strategies
3. Learning
Competencies /
Objectives
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)
a. Factor polynomials with
common monomial factor.
b. Apply the theorems in
proving inequalities in
triangle.
c. Appreciate the concept
about factoring out the
common factor in
polynomials.
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)
a. Factor the difference of
two squares .
b. Solve equations by
factoring the difference of
two squares.
c. Find pleasures in
working with numbers.
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)
a. Find the factors of the
sum or difference of two
cubes.
b. Completely factor a
polynomial involving the
sum and difference of two
cubes.
c. Find pleasures in working
with numbers.
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)
1. Identify a perfect square
trinomial.
2. Get the square of the
numbers.
3. Factor a perfect square
trinomial

2. II. CONTENT Factor of Polynomials
With Common
Monomial Factor(CMF)
Factoring the
Difference of Two
Squares
Factoring the Sum or
Difference of Two
Cubes
Factoring a Perfect
Square Trinomial
III. LEARNING RESOURCES
A. References
1. Teacher’s Guidepages 29-33 pages 34-35 pages 36-37 pages 38-39
2. Learner’s
Materials
pages 27-31 pages 32-33 pages 34-35 pages 36-38
3. Textbook Intermediate Algebra UBD
pages 22-23
Mathematics Activity
Sourcebook pages 22-23
Mathematics Activity
Sourcebook pages 25- 26
Intermediate Algebra UBD
pages 24-25
4. Additional
Materials from
Learning
Resource (LR)
portal
http://lmrds.deped.gov.ph. http://lmrds.deped.gov.ph. http://lmrds.deped.gov.ph. http://lmrds.deped.gov.ph.
B. Other Learning
Resources
Grade 8 LCTG by Dep Ed
Cavite Mathematics 2016
laptop, LCD
Grade 8 LCTG by Dep Ed
Cavite Mathematics 2016
laptop, LCD
Grade 8 LCTG by Dep Ed
Cavite Mathematics 2016
laptop, LCD
Grade 8 LCTG by Dep Ed
Cavite Mathematics 2016
laptop, LCD
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
1. Asking the common
physical features/
behavioural traits among
siblings in the family.
SECRET MESSAGE
Find the square roots and
solve the secret message.
4 = ___ 16 = ___
16 = ___ 81 = ___
49 = ___ 9 = ___
Purpose Setting Activity
So here are the formulas
that summarize how to
factor the sum and
difference of two cubes.
Find the square of the
following:
1. 1 6. 36
2. 4 7. 49
3. 9 8. 81

3. 2. What are the things
common to each set of
pictures?
81 = ___ 25 = ___
16 = ___ 100 = ___
9 = ___ 36 = ___
121= ___ 16 = ___
25 = ___9 = ___
144 = ___ 64 = ___
81= ___ 289 = ___
225 = ___ 49 =___
9 = ___ 81 = ___
25= ___ 16 =___
100= ___ 9 =___
A B C D
16 16 25 1000
E F G H
299 100 400 4
I J K L
36 81 64 81
M N O P
144 100 9 64
Q R S T
49 900 121 4
U V W X
24 9 81 225
Y X
8 9
Study them carefully using
the following diagrams.
Observations:
•For the “sum” case, the
binomial factor on the right
side of the equation has a
middle sign that is positive.
•In addition to the “sum”
case, the middle sign of the
trinomial factor will always
be opposite the middle sign
of the given problem.
Therefore, it is negative.
•For the “difference” case,
4. 16 9. a2
5. 25 10. x4

4. the binomial factor on the
right side of the equation
has a middle sign that is
negative.
•In addition to the
“difference” case, the
middle sign of the trinomial
factor will always be
opposite the middle sign of
the given problem.
Therefore, it is positive.
B. Establishing a
purpose for the lesson
Factoring the common
monomial factor is the
reverse process of monomial
to polynomials.
a(b + c) = ab + ac
Factoring the difference of
two squares is the reverse
process of the product of
sum and difference of two
terms.
(x + y)(x – y) = x2 – y2
Factoring the sum or
difference of two cubes is
the reverse process of
product of binomial and
trinomial.
(x + y)(x2 – xy + y2)
= x3 + y3
(x + y)(x2 + xy + y2)
= x3 - y3
Factoring a perfect square
trinomial is the reverse
process of square o
binomial.
(x + y)2 = x2 + 2xy + y2
(x - y)2 = x2 - 2xy + y2
C. Presenting examples/
instances of the
lesson
a. Factor xy +xz
Get the CMF, x
Divide xy + xz by x
Quotient: y + z
Thus xy + xz = ( y + z)
b. Factor 5n² + 15n
Get the CMF, 5n
Divide 5n² = 15 n by 5n
Quotient: n + 3
Thus 5n² + 15n
= 5n (n + 3)
Factor 4y2 - 36y6
•There is a common factor
of 4y2 that can be factored
out first in this problem, to
make the problem easier.
4y2 (1 - 9y4)
•In the factor (1 - 9y4), 1
and 9y4 are perfect squares
(their coefficients are
perfect squares and their
exponents are even
numbers). Since
subtraction is occurring
1: Factor x3 + 27
Currently the
problem is not written in the
form that we want. Each
term must be written as
cube, that is, an expression
raised to a power of 3. The
term with variable x is okay
but the 27 should be taken
care of. Obviously we know
that 27 = (3)(3)(3) = 33.
Rewrite the original
problem as sum of two
Study the trinomials and
their corresponding
binomial factors.
1. x2 + 10x + 25 = ( x + 5)2
2. 49x2 – 42 + 9
= ( 7x – 3)2
3. 36 + 20 m + 16m2
= (6 + 4m)2
4. 64x2 – 32xy + 4y2
= (8x – 2y)2
a. Relate the first term in
the trinomial to the first

5. c. Factor 27y² + 9y -18
The CMF is 9
Divide 27y² + 9y -18 by 9
The quotient is 3y² + y -2
Thus 27y² + 9y -18
= 9 ( 3y² + y -2)
between these squares, this
expression is the difference
of two squares.
•What times itself will give
1?
•What times itself will give
9y4 ?
•The factors are (1 + 3y2)
and (1 - 3y2).
•Answer:
4y2 (1 + 3y2)(1 - 3y2) or
4y2 (1 - 3y2) (1 + 3y2)
cubes, and then simplify.
Since this is the "sum" case,
the binomial factor and
trinomial factor will have
positive and negative
middle signs, respectively.
x3 + 27 = (x)3 + (3)3
= (x+3)[{x)2 –(x)(3)+(3)2]
=(x+3)(x2-3x+9)
Example 2: Factor y3 - 8
This is a case of
difference of two cubes
since the number 8 can be
written as a cube of a
number, where 8 = (2)(2)(2)
= 23.
Apply the rule for
difference of two cubes, and
simplify. Since this is the
"difference" case, the
binomial factor and trinomial
factor will have negative
and positive middle signs,
respectively.
term in the binomial
factors.
b. Compare the second
term in the trinomial
factor and the sum of the
product of the inner
terms and outer terms of
the binomials.
c. Observe the third term in
the trinomial and the
product of the second
terms in the binomials.
D. Discussing new
concepts and
practicing new skills
#1
Question : What fruit is the
main product of Tagaytay
City? You will match the
products in Column A with
the factors in Column B to
decode the answer.
Factor each of the following:
1. c² - d²
2. 1 - a²
3. ( a + b )² - 4c²
4. 16x² - 4
5. a²b² - 144
Factor the following:
1. x3 – 8
2. 27x3 + 1
3. x3y6 – 64
4. m³ + 125
5. x³ + 343
Supply the missing term to
make a true statement.
1. m2 + 12m + 36
= (m + ___)2
2. 16d2 – 24d + 9
= (4d – ___)2
3. a4b2 – 6abc + 9c2
= (a2b ___)2
4. 9n2 + 30nd + 25d2

6. = (____ 5d)2
5. 49g2 – 84g +36
= ( ______)2
E. Discussing new
concepts and
practicing new skills
#2
Factor the following
1. a²bc + ab²c + abc²
2. 4m²n² - 4mn³
3. 25a + 25b
4. 3x² + 9xy
5. 2x²y + 12xy
Fill in the blanks to make
the sides of each equation
equivalent.
1. ( _____ ) ( x – 9)
= x² -81
2. ( 20 + 4) ( _____ )
= 20² -4²
3. ( _____ ) (2a +3 )
= 4a² - 9
4. ( 6x²y + 3ab)(6x²y -3ab)
= ( _____ ) - 9a²b²
5. ( 13 + x ) (13 – x)
= _____ - x²
Complete the factoring.
1. t3 - w3
= ( t – w ) ( )
2. m3 + n3
= ( m + n ) ( )
3. x3 + 8
= ( x + 2 ) ( )
4. y3 - 27
= ( y – 3 ) ( )
5. 8- v3
= ( 2 – v ) ( )
Factor the following
trinomials.
1. x2 + 4x + 4
2. x2 - 18x + 81
3. 4a2 + 4a + 1
4. 25m2 – 30m + 9
5. 9p2 – 36p + 16
F. Developing mastery
(Leads to Formative
Assessment 3)
Factor the following:
1. 10x + 10y + 10z
2. bx + by + bz
3. 3x³ + 6x² + 9x
4. 10x + 5y –20z
5. 7a³ + 14a² + 21
Factorize the following by
taking the difference of
squares:
1. x2 – 100
2. a2 – 4
3. ab2 – 25
4. 36𝑥2 – 81
5. 54𝑥2 – 6y2
Factor each completely.
a) x ³ + 125
b) a ³ + 64
c) x ³ – 64
d) u ³ + 8
Factor the following:
1. 1. x2 – 5x + 25
2. 2. b2 -10b + 100
3. 36b2 – 12b + 1
4. 49p2 – 56p = 16
5. 49k2 – 28kp + 4p2
G. Finding practical Factor the following Factor the following. Directions. Find the cubeComplete the perfect

7. applications of
concepts and skills in
daily living
1. 16a² + 12a
2. 12am + 6a²m
3. 72x² + 36xy – 27x
4. 5a³ + a³b
5. 30a + 5ay - 25 az
1. 100a2 – 25b2
2. 1 – 9a2
3. 81x2 – 1
4. – 64a2 + 169 b2
5. x2 – 144
roots. Then, match each
solution to the numbers at
the bottom of the page.
Write the corresponding
letter in each blank to the
question.In the survey,
Best place for family picnic
in Tagaytay City?
No 1 2 3 4
27 512 343 216
C R G O
9 10 11
1331 1000 219
I C V
12 13 14
0 64 125
0 E N
12 11 3 5 9
10 7 8 6 13
4
5 6 7 8
1728 8 1 729
P 2 1 1
square trinomial and factor
them.
1. ___ + 16x + 64
2. x2 - ___ + 49
3. x2 + 4x + ___
4. x2 + ___ + 9y2
5. ___ + 10k + 25

8. H. Making
generalizations and
abstractions about the
lesson
Common Monomial Factor
To factor polynomial with
common monomial factor,
expressed the given
polynomial as a product of
the common monomial
factor and the quotient
obtained when the given
polynomial is divided by the
common monomial factor.
The factors of the difference
of two squares are the sum
of the square roots of the
first and second terms times
the difference of their
square roots.
*The factors of 𝑎2 − 𝑏2
=𝑎𝑟𝑒 ( 𝑎 + 𝑏 ) 𝑎𝑛𝑑 ( 𝑎 −𝑏 ).
1. The sum of the cubes of
two terms is equal to
the sum of the two terms
multiplied by the sum
of the squares of these
terms minus the product
of these two terms.
a³ + b³
= ( a + b ( a² - ab + b² )
2. The difference of the
cubes of two terms is
equal to the difference of
the two terms multiplied
by the sum of the
squares of these two
terms plus the product of
these two terms.
a³ - b³
= ( a - b ( a² + ab + b² )
In factoring a perfect
square trinomial, the
following should be noted:
1. The factors are binomials
with like terms
wherein the terms are
the square roots of the
first and the last terms of
the trinomial.
2. The sign connecting the
terms of the binomial
factors is the same as
the sign of the middle
term of the trinomial.
I. Evaluating learning Factor the following:
1. 5x + 5y + 5z
2. ax + ay + az
3. 4x³ + 8x² + 12x
4. 6x + 18y – 9z
5. 3a³ + 6a² + 12
Factorize the following by
taking the difference of
squares:
1. x2 – 9
2. a2 – 1
3. ab2 – 16
4. 16𝑥2 – 49
5. 54𝑥2 – 6y2
Supply the missing
expression.
1. 𝑚3 - 27
= (m – 3) _________
2. 64 + 27𝑛3
= ____(16 – 12n + 9𝑛2 )
3. _______
= ( 2p + 5q ) ( 4𝑝2 – 10pq +
25𝑞2 )
4. 𝑥6 + 1000
= _____𝑥4 - 10𝑥2 + 100 )
Factor the following:
3. 1. x2 – 6x + 9
4. 2. b2 -12b + 36
3. 4b2 – 4b + 1
4. 49p2 – 56p = 16
5. 49k2 – 28kp + 4p2

9. 5. ________
= ( 6x – 7y ) ( 36𝑥2 + 42xy +
49𝑦2 )
J. Additional activities for
application or
remediation
A. Follow up
Supply the missing term
1. 3a + 3b = ____ (a + b)
2. bx + by + bz
= _____ (x + y + z)
3. a²b - ab² = ab (_____
4. 4x + 6y = ____(2x + 3y )
5. m³ - m = ____(m² - 1)
B. Study Factoring
Polynomials
1. What is a common
monomial factor?
2. How will you factor
polynomial by grouping?
Reference: G8 Mathematics
Learner’s Module pages
45-46
Factorize the following by
taking the difference of
squares:
1. x2 – 9
2. a2 – 1
3. ab2 – 16
4. 16𝑥2 – 49
5. 54𝑥2 – 6y2
Solve the following:
1. The product of two
consecutive even
integers is 528. Find the
value of each integer.
Complete the perfect
square trinomial and factor
them.
1. ___ + 16x + 64
2. x2 - ___ + 49
3. x2 + 4x + ___
4. x2 + ___ + 9y2
5. ___ + 10k + 25
V. REMARKS
VI. REFLECTION
1. No.of learners who
earned 80% on the
formative assessment
2. No.of learners who
require additional
activities for

10. remediation.
3. Did the remedial
lessons work? No.of
learners who have
caught up with the
lesson.
4. No.of learners who
continue to require
remediation
5. Which of my teaching
strategies worked well?
Why did these work?
6. What difficulties did I
encounter which my
principal or supervisor
can help me solve?
7.