A semi-detailed lesson plan on factoring polynomial with common monomial factor

1. Republic of the Philippines
Department of Education
Region VII Central Visayas
Division of Cebu City
Quiot National High School
Bogo, Quiot, Cebu City
A Semi-Detailed Lesson Plan
In Math 8
___________________
Date of Teaching
____________________
Time of Teaching
Quiot National High School- Afternoon Session
Venue of Teaching
Prepared by:
LORIE JANE L. LETADA
Teacher 1
Observed by:
ELEANOR D. GALLARDO
ASSISTANT PRINCIPAL

2. I. Intended Learning Outcomes
Through varied learning activities, the grade 8 students with at least80 % ofaccuracy shall
able to:
1. Define common monomial factoring
2. Factor polynomials with common monomial factor
3. Relate the importance of factoring polynomials with common monomial factor
II. Learning Content
A. SubjectMatter
Factoring Polynomials with Common Monomial Factor
B. Skill Focus
C. Reference
Diaz, Z., Mojica M. (2013) . Next Century Mathematics 8; Quezon City ; Phoenix
Publishing House , Inc; Mathematics 8 Learner’s Module K-12; DepEd K-12 Modified
Curriculum Guide and Teacher’s Guide for Mathematics 8
http://www.math.com/school/subject1/lessons/S1U4L2DP.html
https://quickmath.com/math-tutorials/common-monomial-factors-factoring-special-
products-and.html
D. Materials
Learners’ Module; Google Classroom; powerpointpresentation; google forms
III. Learning Experiences
A. Activity
The students will identify the common things that found in the picture.

3. The GCF of these three monomials is (3)(x)(x) = 3 𝒙 𝟐
B. Analysis
 What are the things common in this picture?
 Are there things that make them different?
 Can you spotthings that are found on one picture butnot to the other three?
 What are the things common to two pictures but are not found on the other?
C. Abstraction
Common monomial factoring is the process of writing a polynomial as a product of
two polynomials, one of which is a monomial that factors each term of the polynomial.
To ensure that the polynomial is the prime polynomial, use the Greatest Common
Factor (GCF) of the terms of the given polynomials
1. Find the GCF of 4𝒎 𝟐 and 𝟏𝟎𝒎 𝟒.
Solution:
Express each as a product of prime factors.
4𝒎 𝟐 = 2 (2) m m
𝟏𝟎𝒎 𝟒 = (5) 2 m m (m) (m)
Common Factors = 2 m m
The GCF of these two monomials is (2)(m)(m) = 𝟒𝒎 𝟐
2. Find the GCF of 𝟔𝒙 𝟒 , 9𝒙 𝟐y, and 𝟏𝟓𝒙 𝟓 𝒚.
Solution:
Express each as a product of prime factors.
𝟔𝒙 𝟒 = (2 ) 3 x x (x) (x)
9𝒙 𝟐 y = (3) 3 x x (y)
𝟏𝟓𝒙 𝟓 𝒚 = (5) 3 x x (x) (x) (x) (y)
Common Factors = 3 x x
Now, you are ready to find the factor of polynomials with common monomial.
Observe and analyze the steps:
1. Find the greatest common factor (GCF) of the terms in the polynomial. This is
the first factor.
2. Divide each term by the GCF to get the other factor.
Factor each expression.
1. 𝟏𝟎𝒚 𝟒 + 5𝒚 𝟑
Step 1 : Find the GCF.
𝟏𝟎𝒚 𝟒
= (5) (2) (y) (y) (y) (y)
5𝐲 𝟑
= (5 ) (y) (y) (y)
GCF = 5 y y y
GCF = 𝟓𝒚 𝟑
Step 2: Divide out the common factor.
𝟏𝟎𝒚 𝟒
+ 5 𝒚 𝟑
= 𝟓𝒚 𝟑
(
𝟏𝟎𝒚 𝟒
𝟓𝒚 𝟑 +
𝟓𝒚 𝟑
𝟓𝒚 𝟑 )
= 𝟓𝒚 𝟑
(𝟐𝒚 𝟒−𝟑
+ 𝟏
= 𝟓𝒚 𝟑
(𝟐𝒚 + 1 )

4. 2. 𝟐𝟓𝒃 𝟑 𝒄 𝟐 − 5𝒃 𝟐 𝒄
D. Application
1. Find the GCF of 8𝒚 𝟔 and 𝟏𝟎𝒚 𝟒z.
Solution:
Express each as a product of prime factors.
8𝒚 𝟔 =
𝟏𝟎𝒚 𝟒z =
Common Factors =
2. Find the GCF of 𝟐𝟎𝒃 𝟒 𝒄 , 5𝒃 𝟐c, and 𝟏𝟓𝒃 𝟑 𝒄.
Solution:
Express each as a product of prime factors.
𝟐𝟎𝒃 𝟒 𝒄 =
5𝒃 𝟐c =
𝟏𝟓𝒃 𝟑 𝒄 =
Common Factors =
𝟑.. 𝟏𝟐𝒉 𝟒 𝒊 𝟐 − 15𝒉 𝟐 𝒊
Step 1 Find the GCF.
𝟐𝟓𝒃 𝟑 𝒄 𝟐 = (5)(5)(b)(b)(b)(b)(c)(c)
𝟓𝒃 𝟕 𝒄 = (3) (5)(b)(b) (c)
GCF = (5)(b)(b) (c)
GCF = 5𝒃 𝟐 𝒄
Step 2 Divide out the common factor.
𝟐𝟓𝒃 𝟑 𝒄 𝟐 − 5𝒃 𝟐 𝒄= 5𝒃 𝟐 𝒄 ( 𝟐𝟓𝒃
𝟑
𝒄 𝟐
𝟓𝒃
𝟐
𝒄
−
𝟓𝒃
𝟐
𝒄
𝟓𝒃
𝟐
𝒄
)
= 5𝒃 𝟐 𝒄 ( 5𝒃 𝟑−𝟐 𝒄 𝟐−𝟏 – 1)
=5𝒃 𝟐 𝒄 ( 5b – 1 )
Any
number or
variables
divided by
itselfis
always
equal to
1.
All
variables
always
have
imaginary
exponent
one.
Step 1 Find the GCF.
𝟏𝟐𝒉 𝟒 𝒊 𝟐=
15𝒉 𝟐 𝒊 =
GCF =
GCF =
Step 2 Divide out thecommon
factor.
𝟏𝟐𝒉 𝟒
𝒊 𝟐
− 15𝒉 𝟐
𝒊 =
=
=

5. IV. Evaluation
Factor each expression. Show your solution with the step-by-step process.
𝟏. 𝟖𝒈 𝟔
+ 16𝒈 𝟐
4. 𝟔𝒂 𝟐
𝒃+ 𝟏𝟖𝒂𝒃
𝟐. 𝟒𝟗𝒚 𝟗
+ 21𝒚 𝟐
5. 𝟐𝟒𝒑 𝟏𝟗
𝒒 𝟏𝟐
+ 𝟒𝒑 𝟏𝟓
𝒒 𝟕
𝟑. 𝟐𝒙 𝟐
𝒚 𝟐
− 14y 6. 𝟑𝟎𝒓 𝟔
+ 𝟏𝟎𝒓 𝟐
E. Assignment
Skill Booster!