8
Department of Education
National Capital Region
S CHOOLS DIVIS ION OFFICE
MARIK INA CITY
MATHEMATICS
Quarter 1: Module 1
Introduction to Factoring Polynomials
Writer:
John Anthony P. Santos
Cover Illustrator:
Joel J. Estudillo
1
DISCIPLINE • GOOD TASTE • EXCELLENCE
What I Need to Know
Hello Grade 8 learners! In this module you will learn how to:
•
factor completely different types of polynomials (polynomials with
common monomial factor, difference of two squares). M8AL-Ia-b-1
You can say that you have understood the lesson in this module if you can:
1.
2.
3.
4.
find the greatest common factor of a given number.
identify prime factors of polynomials.
factor polynomials by finding common monomial factor.
factor difference of two squares.
What I Know
Choose the letter that correspond to the correct answer.
1. Find the greatest common factor of 24, 64, 108.
A. 2
B. 4
C. 8
D. 24
2. What is the greatest common factor of the monomials a3b3 and a2b5?
A. a2b3
B. a2b5
C. a3b3
D. a3b5
3. What is the greatest common factor of the polynomial 30w 3 + 48w + 12w2?
B. 6w3
A. 6w
D. 12w3
C. 12w
4. What is the factored form of 56a3 – 8a?
A. 8a (7a3 – a)
B. 8a2 (35a2 – a)
C. 8a (7a2 – 1)
D. 8a2 (56a3 – 8a)
5. Complete the factor of 7x2y5 + 56x2y4 = 7x2y4 ( ______ ).
A. y + 8
B. 7y + 8x
C. y + 8x2
D. x2y + 8
C. 484
D. 49
6. Multiply (25 – 7) (25 + 7).
A. 625
B. 576
7. Which of the following polynomials can be factored using the difference of
two squares formula?
A. x2 + 16
B. 25 – y2
C. x3 + 1
D. x3 – 27
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DISCIPLINE • GOOD TASTE • EXCELLENCE
8. When factored, the expression 16x2 – 25y2 is equivalent to __.
A. (4x – 5y) (4x + 5y)
C. (4x – 5y) (4x - 5y)
B. (8x – 5y) (8x + 5y)
D. (8x – 5y) (8x - 5y)
9. Factor 16x2 – 100.
A. (2x – 5) (2x + 5)
C. 4(2x – 5) (2x + 5)
B. 4(2x – 10) (2x + 10)
D. 4(4x – 5) (4x + 5)
10. Factor x4 – y4 completely.
A. (x2 – y2) (x2 – y2)
C. (x – y) (x + y) (x2 + y2)
B. (x2 – y2) (x2 + y2)
D. (x – y) (x + y) (x2 - y2)
Lesson 1. POLYNOMIALS WITH COMMON MONOMIAL FACTOR
What’s In
When you were in elementary, you have already learned about
factoring.
A. Find the GCF of the following numbers by making a list.
1. 18 and 36 GCF: ______
4. 16, 40 and 56 GCF: ______
2. 30 and 42 GCF: ______
5. 42, 49 and 70 GCF: ______
3. 42 and 49 GCF: ______
B. Find the GCF of the following numbers using prime factorization.
1. 42 and 56 GCF: ______
4. 64, 48 and 16 GCF: ______
2. 37 and 51 GCF: ______
5. 48, 64 and 32 GCF: ______
3. 49 and 77 GCF: ______
C. Identify the factors and the product in each problem.
Note: Numbers 1 and 2 are already done for you.
1. 4(5) = 20
factors: 4,5
product: 20
2. 5(2 x2) = 10x2
factors: 5, 2 x2
product: 10x2
3. 2(7x2y) = 14x2y
factors: ______
product: ______
4. 3a(7a2b3) = 12a3b3
factors: ______
product: ______
5. -5b3c2(11c2) = -55b3c4
factors: ______
product: ______
6. 13m3n(3mn) = 39m4n2
factors: ______
product: ______
7. -17(-3klm2) = 51klm2
factors: ______
product: ______
2
DISCIPLINE • GOOD TASTE • EXCELLENCE
What’s New
Marikina City is known for its
different festives like the “AngkanAngkan.” Are you familiar with this annual
event? This festivity instills -the values of
length of connection and solidarity and is
celebrated for seven days with the theme
of “Ka-angkan Ko, Mabuting Tao.”, More
so, festivity showcased more advances
with regard to the qualities and great
characteristics of Marikeños.
https://www.facebook.com/photo.php?fbid=218943521113
9254&set=a.2189431851139590&type=3&theater
If you have watched any parade like Angkan-Angkan, Rehiyon-Rehiyon,
and others, then answer the following:
1. Can you describe how they were arranged or organized?
2. What are the things that are common to the parade that you have
watched?
3. Can you identify things that you observed common in the parade?
4. Why do you think it is useful to find what is common to two or more
things?
5. Why is it important to know the commonality of the different things
around us?
Now, if you are one of the organizers of the said festival or activity, what
aspect/s in the parade will you consider for a much better output or result of the
program?
In this lesson, you will learn how to break down an expression into their
commonality and answer the questions: (a)What is greatest common
monomial factor? (b)How to find the greatest common monomial factor?
What is It
A common method of factoring numbers is to completely factor the
number into positive prime factors. A prime number is a number whose only
positive factors are 1 and itself.
In polynomials, the first method for factoring will be factoring out the
greatest common factor. This is generally the first thing that we should try as
it will often simplify the problem.
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DISCIPLINE • GOOD TASTE • EXCELLENCE
But prior to that, you have to recall these: A monomial is a type of
polynomial expression that is the product of constants and nonnegative integer
powers of variables, like 2, −4x2 , abc, and −2e2f3g5. While the other types of
polynomials are binomial, trinomial, and multinomial.
And to factor a polynomial with common monomial expressions, first, we
have to factor the numerical coefficient into positive prime factors completely.
Simply write the complete factorization of each monomial and find the common
factors.
Example 1: The GCF of 12, 18, and 36. The GCF is 6.
Example 2: The GCF of 10x3 and 4x.
10x3 = 2⋅5⋅x⋅x⋅x
4x = 2⋅2⋅x Therefore, the GCF is 2x
What you’ve learned in the examples are all about the greatest common
factor (GCF) and how to find this for monomials.
Proceed to Factor Polynomials with common monomial factor.
How to use this method?
To use this method we have to look at all the terms and determine if there
is a factor that is in common to all the terms. If you notice that there is a
common factor, then factor it out in the polynomial. Example 3: Factor 6ab +
18bc
6ab = 2⋅3⋅a⋅b
Express as prime factors
18bc = 2⋅3⋅3⋅b⋅c
The common factors are 2⋅3⋅b.
Therefore, the GCF is, 6b.
6ab + 18bc = (6b⋅a + 6b⋅3c)
=
6𝑏⋅𝑎
6𝑏
+
6𝑏⋅3𝑐
6𝑏
Take out the GCF, then divide the polynomial using the
GCFas divisor to get the other factor.
= a + 3c The other factor of the given polynomial 6ab + 18bc.
= 6b (a + 3c)
The factored form of 6ab + 18bc
Example 4: Factor 4r2s3 - 8s2t.
Step 1: Express each term of the given polynomial as prime factors.
4r2s3 = 22 · r2 · s2 · s
8s2t = 22 ·2 · s2 · t
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DISCIPLINE • GOOD TASTE • EXCELLENCE
Step 2: Determine the GCF.
4r2s3 = 22 · r2 · s2 · s
8s2t = 22 ·2 · s2 · t
GCF is 4s2.
Step 3: Divide each term of the given polynomial by their GCF.
4𝑟 2 𝑠 3
4𝑠 2
−
8𝑠 2𝑡
= r2s – 2t
4𝑠 2
Factored form of 4r2s3 - 8s2t is 4s2 (r2s – 2t)
ANSWER: 4s2 ( r2s – 2t )
Note: The resulting expression is in factored form because it is written as a
product of two polynomials, whereas the original expression is a twotermed sum.
Here are the steps in factoring polynomials with GCMF:
1. Find the greatest common monomial factor (GCMF). The largest
monomial that is a factor of each term of the polynomial
2. Factor it out, then divide the polynomial by the factor found in step 1. The
quotient is the other factor.
3. Express the polynomial as the product of two factors (the GCF and the
quotient).
Remember:
The distributive property of multiplication over addition
𝒂 (𝒃 + 𝒄) = 𝒂𝒃 + 𝒂𝒄
In factoring out the greatest common factor we do its reverse.
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DISCIPLINE • GOOD TASTE • EXCELLENCE
What’s More
ACTIVITY 1: Find all the prime factors of the given polynomials.
Polynomials
Factors
1. 30xy
2. 42ab2
3. 56a3b4
4. 49ab5
5. 70a3b3
ACTIVITY 2: Find the greatest common factor of the given polynomials.
Polynomials
GCF
1. 24y and 30xy
2. 42ab3 and 70a2b2
3. 6x3, 24x2 and 8x
4. 16a2b2, 40a2b3, and 56a3b4
5. 70a3b3, 49ab5 and 42a2b4
ACTIVITY 3: Factor each polynomial completely.
Express each polynomial as factors by getting their GCF.
1. 12x + 8y
4. 12x + 15xy + 21x2
2. 70x5y3 – 42x8y2
5. 24a3b2 + 36a2b4 – 60a4b3
3. 18x2 + 45x
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DISCIPLINE • GOOD TASTE • EXCELLENCE
What I Have Learned
Fill in the blanks with the appropriate term/s.
The _________ is the largest monomial that is a factor of each term of
the polynomial.
To factor polynomials with GCMF:
1. Find the ________, the largest monomial that is a factor of each term
of the polynomial.
2. Factor it out then, _______ the polynomial by the factor found in step 1.
The ________ is the other factor.
3. Express the polynomial as the ________ of two factors (the GCMF and
the quotient).
7
DISCIPLINE • GOOD TASTE • EXCELLENCE
What I Can Do
Part of the celebration of the “Angkan-Angkan Festival” is the Salusalo of Kaangkan or clans which is often held at the open grounds space inside
the Marikina Sports Center. Each clan occupies an allotted square portion of
the venue.
Solve the problem using the adjoining UPS Check chart below.
UNDERSTAND
PLAN
What is happening in the problem?
What is the question asking you to find?
What information is needed to solve the
problem?
Estimate a reasonable solution.
Draw your model.
SOLVE
The area of a square lot allotted to each
clan is numerically equal to its perimeter.
Find the length of a side of a square lot.
CHECK
Show all your thinking to solve the Does my answer make sense? Is my
estimate correct? Did I answer the
problem.
question?
Explain your thinking to justify your
answer.
8
DISCIPLINE • GOOD TASTE • EXCELLENCE
Rubric for the activity below:
1
2
3
Computation
The answer and
strategies used were
incorrect.
The answer is
incorrect, but the
strategy used to
solve is correct.
The answer and
strategies used to
solve are correct.
Label
The answer does not
include a label.
The answer includes
a label but it is not
accurate.
The answer includes
an accurate label.
Visual
Representation
Work does not
include a label.
Work includes a
visual representation
but it includes errors.
Work includes
accurate pictures,
number lines and/or
equations.
Explanation
No written
explanation is
included.
Explanation is
included but not
detailed or in
complete sentences.
Explanation is
detailed and written
in complete
sentences.
Work is not legible.
Work is difficult to
read but legible.
Work is neat and
legible.
Neatness
Assessment
Choose the letter that corresponds to the correct answer.
1. Find the greatest common factor of 24, 64, 108.
A. 2
B. 4
C. 8
D. 24
2. What is the product of 3𝑥 2 𝑦 and 15𝑥𝑦 2 ?
A. 30𝑥 2 𝑦 2
B. 45𝑥 2 𝑦 2
C. 60𝑥 2 𝑦 2
D. 45𝑥 3 𝑦 3
C. a3b3
D. a3b5
3. What is the GCF of a3b3 and a2b5?
A. a2b3
B. a2b5
4. The GCF of 14x7 and 10x4 is __________.
B. 2x4
A. 2x
C. 2x7
D. 10x4
5. What is the GCF of 30w3 + 48w + 12w2?
A. 6w
B. 6w3
C. 12w
D. 12w3
B. 2f 2(1 – 3f)
C. 2f 3(8 – 6f 2)
D. 3f(1 – 3f)
6. Factor 2f 2 – 6f 3.
A. 2f 2(f – 3f 2)
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DISCIPLINE • GOOD TASTE • EXCELLENCE
7. The factored form of 56a3 – 8a is __________.
A. 8a(7a3 – a)
C. 8a(7a2 – 1)
B. 8a2(35a2 – a)
D. 8a2(56a3 – 8a)
8. Find the GCF of the terms: -a9b5 and -ab4
A. a9b5
B. b4
C. ab4
D. a9b4
9. Complete the factors of 7x2y5 + 56x2y4 = 7x2y4 ( _____ ).
A. y + 8
B. 7y + 8x
C. y + 8x2
D. x2y + 8
10. Factor the polynomial 16x9y9 – 24x6y7 – 16x3y2.
A. 8x3(2x6y9 – 3x3y7 – 2y2)
C. 8x3y2(2x6y7 – 3x3y5 – 2)
B. No common factor except 1
D. 8(2x9y9 – 3x6y7 – 2x3y2)
Additional Activities
Factor the following polynomials using GCMF:
1) 6v2 – 26v + 20
2) 4ef2 - 4e2f2 + e3f2
3) 12a3 + 9a2 + 15a
4) 13b + 26b2 – 39b3
5) 18x2y4 – 12x2y3 + 24x2y2
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DISCIPLINE • GOOD TASTE • EXCELLENCE
Lesson 2. DIFFERENCE OF TWO SQUARES (DOTS)
What’s In
At this point, you have already learned how to factor polynomials using
their greatest common monomial factor. You can now proceed to the next type
of factoring which is the difference of two squares.
To check if you have enough knowledge about the next lesson, try to
answer the questions indicated below.
A. Square the following numbers:
22 = ____
52 = ____
92 = ____
162 = ____
B. Find the principal root of the numbers:
√4 = ____ √25 = ____ √81 = ____ √256 = ____
C. Simplify the following:
52 – 22 = _______
(9 + 2) (9 – 2) = _______
162 – 92 = _______
(16 + 5)(16 – 5) = ______
What’s New
Marikina City is known to be the shoe capital of the Philippines. Have
you ever visited any shoe shops in this city? Have you observed how the shoes
are arranged inside the stores? Why do you think they are arranged that way?
In support to the local sapateros of the City of
Marikina, the Marikina Cultural, Tourism, Trade and
Investment Promotion Office will exhibit the shoe
products of the 300 registered shoe and leather
manufacturers in the city. The proposed alloted space
for the exhibit is the freedom park. Organizers will
install a façade inside the parameter of the said park
and shall be divided equally for the participants.
https://d0ctrine.com/2019/01/09/s
hoes-made-in-marikina/
11
DISCIPLINE • GOOD TASTE • EXCELLENCE
1. How will you arrange the 300 pair of shoes for each façade? Will you
arrange it by size? By color? By its type of material? By its style?
2. How many partitions per façade will you create assuming that there are four
square facades given that the area of each façade measures 9 m2?
3. How much area will be alotted for each shoe manufacturer?
4. What are the things will you consider in looking for dimensions?
5. What mathematical concepts would you consider in forming different
dimensions? Why?
6. Consider that, if the length or the width of one side is increased or
decreased by unknown quantities (x), how could you represent the
dimensions?
What is It
The product of the sum and difference of two polynomials is unique in
the sense that its middle term vanishes. Since factoring is the reverse of finding
the product, the difference of two squares is therefore, the product of the sum
and difference of the square roots.
That is, x2 – y2 = (x + y)(x– y)
How do we factor the difference of two squares of polynomials?
Here are the steps in factoring polynomials as DOTS:
● Find the greatest common monomial factor (GCMF), if any.
● Express each term using the pattern, x2 – y2 = (x + y)(x– y)
Which is the sum and difference of the square roots of the first and the
last terms.
● Check the results.
Example 1: Factor x2 – 36y2
(1) The polynomial x2 – 36y2 is obviously the difference of two squares
without common factor.
(2) Therefore, x2 – 36y2 = x2 – 36y2
= (x)2 - (6y)2
= (x + 6y)(x - 6y).
12
DISCIPLINE • GOOD TASTE • EXCELLENCE
To further check the factors, use Distributive Property of Equality.
To do this, multiply (x) and (x - 6y), thus we have x2 - 6xy, then multiply (6y)
and (x - 6y), we have 6xy - 36y2 and the next step is to get the sum of the
products,
(x2 – 6xy) + (6xy + 36y2) = x2 – 6xy + 6xy – 36y2
= x2 – 36y2
Notice that we do not have a middle term, this is because when we add
–6xy and +6xy the sum is zero (0).
Example 2: Factor 4a2x2– 25b2x2 completely.
(1) The polynomial 4a2x2– 25b2x2 contains a common factor x2.
4a2 x2– 25b2 x2 = x2 (4a2 – 25b2). Since (4a2 – 25b2) is still
factorable using the pattern.
(2) Follow the pattern for 4a2 – 25b2 = (2x)2 - (5b)2
(3) Therefore, 4a2 x2– 25b2 x2 = x2(2a + 5b)(2a – 5b).
16
Example 3: Factor 49 − 25𝑥 2
(1) The polynomial is obviously the difference of two squares without common
factor.
(2) The first term
(3) Therefore,
16
49
16
49
4
= ( )2 , the second term 25x2 = (5x)2.
7
4
4
− 25𝑥 2 = (7 + 5x)( 7 – 5x)
(4) Check the results using FOIL method.
13
DISCIPLINE • GOOD TASTE • EXCELLENCE
What’s More
Split Me!
Factor the following polynomials completely.
1. a2 – 4
2. 25s2 – t2
3. 9x2 – 16y2
4. 16a2b2c2 – 25c4
5. 4x2a – 25y4
6. m4 – 1
7. 100 – 16b4
8. 36 – (a-b)2
9. [16 – (a + b)2]
10. (m–n)2 - (m + n)2
What I Have Learned
How did you factor the difference of two squares?
Write the steps: ____________________________
____________________________
____________________________
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DISCIPLINE • GOOD TASTE • EXCELLENCE
What I Can Do
Solve the problem using the adjoining UPS Check chart below.
UNDERSTAND
PLAN
What is happening in the problem?
What is the question asking you to find?
What information is needed to solve the
problem?
Estimate a reasonable solution.
Draw your model.
SOLVE
The area of the two square facades to be used in the
shoe exhibit in Marikina Freedom Park is 20 square
meters. Each side of one square façade is twice as long
as a side of the other square facade. Find the lengths of
the sides of each square wall.
CHECK
Show all your thinking to solve the Does my answer make sense? Is my
estimate correct? Did I answer the
problem.
question?
Explain your thinking to justify your
answer.
Rubric for the activity below:
1
2
3
Computation
The answer and
startegies used were
incorrect.
The answer is incorrect,
but the strategy used to
solve is correct.
The answer and
strategies used to
solve are correct.
Label
The answer does not
include a label.
The answer includes a
label but it is not accurate.
The answer includes
an accurate label.
Work does not include a
label.
Work includes a visual
representation but it
includes errors.
Work includes
accurate pictures,
number lines and/or
equations.
No written explanation
is included.
Explanation is included but
not detailed or in complete
sentences.
Explanation is detailed
and written in complte
sentences.
Work is not legible.
Work is difficult to read but
legible.
Work is neat and
legible.
Visual
Representation
Explanation
Neatness
15
DISCIPLINE • GOOD TASTE • EXCELLENCE
Assessment
Choose the letter that corresponds to the correct answer.
1. Multiply (25 – 7) (25 + 7).
A. 625
B. 576
C. 484
D. 4
C. 𝑥 2
D. 9
2. Expand: (x + 3) (x – 3).
A. 𝑥 2 − 9
B. 𝑥 2 + 9
3. Which of the following polynomials can be factored using the difference of
two squares formula?
B. 25 – y2
A. x2 + 16
C. x3 + 1
D. x3 – 27
4. Which expression is equivalent to 9x2 – 16?
A. (3x + 4)(3x - 4) B. (3x - 4)(3x - 4)
C. (3x + 8)(3x - 8)
D. (3x - 8)(3x - 8)
5. When factored, the expression 16x2 – 25y2 is equivalent to __________.
A. (4x – 5y) (4x + 5y)
C. (4x – 5y) (4x - 5y)
B. (8x – 5y) (8x + 5y)
D. (8x – 5y) (8x - 5y)
6. The factored form of 36 – x6 is ___________.
A. (x3 + 6) (x3 - 6)
C. (6 – x3) (6 + x3)
B. (x6 + 6) (x6 - 6)
D. (6 + x6) (6 – x6)
7. Factoring 16x2 – 100 gives ____________.
A. (2x – 5) (2x + 5)
C. 4(2x – 5) (2x + 5)
B. 4(2x – 10) (2x + 10)
D. 4(4x – 5) (4x + 5)
8. Which of the following expressions is not a factor of 16x 4 – 81y4?
A. 2x – 3y
B. 2x + 3y
C. 4x – 9y
D. 4x2 - 9y2
9. Factor x4 – y4 completely.
A. (x2 – y2) (x2 – y2)
C. (x – y) (x + y) (x2 + y2)
B. (x2 – y2) (x2 + y2)
D. (x – y) (x + y) (x2 - y2)
10. Let M = (2x – 7)(2x + 7), and let N = 4x2 – 49. If x = 3, which statement is
true about M and N?
A. M > N
B. M < N
C. M = N
D. M ≠ N
16
DISCIPLINE • GOOD TASTE • EXCELLENCE
Additional Activities
Factor the polynomials completely:
1. 𝑥 4 − 1
2. 7𝑥 5 − 7𝑥
3. 2y – 2yz2
4. 4c4 – 4c2
5. – 98 + 2a2
17
DISCIPLINE • GOOD TASTE • EXCELLENCE
SUMMATIVE TEST
Choose the letter that corresponds to the correct answer.
1. Which is the product of 3𝑥 2 𝑦 and 15𝑥𝑦 2 .
A. 30𝑥 2 𝑦 2
B. 45𝑥 2 𝑦 2
C. 60𝑥 2 𝑦 2
D. 45𝑥 3 𝑦 3
B. 2x4
C. 2x7
D. 10x4
B. 2f2 (1 – 3f)
C. 2f3 (8 – 6f2)
D. 3f (1 – 3f)
2. The GCF of 14x7 and 10x4 is ______.
A. 2x
3. Factor 2f2 – 6f3.
A. 2f2 (f – 3f2)
4. Find the GCF of -a9b5 and -ab4.
A. a9b5
B. b4
C. ab4
D. a9b4
5. Factor the polynomial 16x9y9 – 24x6y7 – 16x3y2.
A. 8x3 (2x6y9 – 3x3y7 – 2y2)
C. 8x3y2 (2x6y7 – 3x3y5 – 2)
B. No common factor except 1
D. 8 (2x9y9 – 3x6y7 – 2x3y2)
6. Expand: (x + 3) (x – 3).
A. 𝑥 2 − 9
B. 𝑥 2 + 9
C. 𝑥 2
D. 9
7. Which expression is equivalent to 9x2 – 16?
A. (3x + 4) (3x - 4)
C. (3x - 4) (3x - 4)
B. (3x + 8) (3x - 8)
D. (3x - 8) (3x - 8)
8. The factored form of 36 – x6 is __.
A. (x3 + 6) (x3 - 6)
C. (6 – x3) (6 + x3)
B. (x6 + 6) (x6 - 6)
D. (6 + x6) (6 – x6)
9. Which of the following expressions is not a factor of 16x 4 – 81y4?
A. 2x – 3y
B. 2x + 3y
C. 4x – 9y
D. 4x2 – 9y2
10. Let M = (2x – 7)(2x + 7), and N = 4x2 – 49. If x = 3, which statement is true
about M and N?
A. M > N
B. M < N
C. M = N
D. M ≠ N
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DISCIPLINE • GOOD TASTE • EXCELLENCE
Development Team of the Module
Writer:
John Anthony P. Santos – SNNHS
Editors:
Gemo Parajas (BNNHS)
Bielynda Daelo – JDPNHS
Analyn C. Santos – MSHS
Violentina J. Asuncion – PHS
Marites M. Bendoy – THS
Amor Agarro – MHS
Joel Estudillo – SNNHS
Lourdes B. Guyong – NHS
Internal Reviewer: Dominador J. Villafria (Education Program Supervisor-Mathematics)
Cover Illustrator: Joel J. Estudillo (SNNHS)
Management Team:
Sheryll T. Gayola
Assistant Schools Division Superintendent
OIC, Office of the Schools Division Superintendent
Elisa O. Cerveza
Chief, CID
OIC, Office of the Assistant Schools Division Superintendent
Dominador J. Villafria
Education Program Supervisor-Mathematics
Ivy Coney A. Gamatero
Education Program Supervisor– LRMS
For inquiries or feedback, please write or call:
Schools Division Office- Marikina City
Email Address: sdo.marikina@deped.gov.ph
191 Shoe Ave., Sta. Elena, Marikina City, 1800, Philippines
Telefax: (02) 682-2472 / 682-3989
DISCIPLINE • GOOD TASTE • EXCELLENCE