(toc) Table of Contents
The learner demonstrates understanding of key concepts of factors of polynomials (Polynomials with common monomial factor)
The learner is able to formulate real-life problems involving factors of polynomials (with common monomial factor)
Factors completely different types of polynomials (polynomials with common monomial factor), M8AL-Ia- b-1
I. OBJECTIVES
Identifies the common monomial factor of the given polynomials
II. CONTENT
Factoring polynomials with common monomial factor
III. LEARNING RESOURCES
Teacher’s Guide (TG) in Mathematics 8, pp. 32 – 34
Our World of Math (Textbook) in math 8, pp. 10 – 13,
Moving Ahead With Mathematics 8, pp. 194 – 195
Elementary Algebra, pp. 182 - 184
IV. PROCEDURES
A. Reviewing or presenting the new lesson
ACTIVITY: PICTURE ANALYSIS
(alert-success)The teacher will provide at least three pictures.
- Divide the class into five groups (each group will use THINK, PAIR and SHARE strategy).
- Provide each group with pictures.
- Let the learners identify the difference of the picture
- What is/are the picture?
- What have you observed on the picture?
- Did you find any common?
- Process all groups’ answers.
B. Establishing a purpose for the lesson
Motive Questions:
1. What are the things common to these pictures?
2. Are there things that make them different?
3. What is/are the thing/s common to two pictures but not found on the other? (answers may vary)
(alert-success)The teacher must lead the students to the concept of “Factoring with the common monomial factor” (answers may vary)
C. Presenting examples of the new lesson
ACTIVITY: Do we have a common?
Identify the common term of each polynomial through prime factorization.
1. $2ab{\rm{ }} + {\rm{ }}2ac$
Ans. $2a$
2. $20{x^2} - 12x$
Ans. $4$
3. $x(a - b) + y(a - b)$
Ans. $(a - b)$
Ask the following:
- What are the prime factors of each term?
- What is the common factor?
- How did you identify the common factor?
D. Discussing new concepts and practicing new skills #1
BIG IDEA!
The teacher will discuss this statement.
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. Every expression has itself and the number $1$ as a factor. These are called the trivial factors. If a monomial is the product of two or more variables or numbers, then it will have factors other than itself and $1$. Note: teacher will provide at least three examples.
E. Discussing new concepts and practicing new skills #2
ACTIVITY: Match it to me!
Instructions: Match the polynomial in column A to its factors in column B.
| A | B |
|---|---|
| 1. ${\rm{x}}{{\rm{ }}^3}{\rm{ y}}{{\rm{ }}^2}{\rm{ + xy}}{{\rm{ }}^3}{\rm{ + 2x}}{{\rm{ }}^2}{\rm{ y}}{{\rm{ }}^3}$ |
a. $x{y^2}({x^2} + y + 2xy)$ |
| 2. ${x^2} + {x^2}y + x{y^2}$ |
b. $3({y^2}-5x-4)$ |
| 3. $3{y^2}-15y-12$ | c. $xy({x^2}+x+y$ |
Answer to the activity:
- a
- c
- b
(alert-success) Teacher will discuss how the factors of the polynomials obtain.
F. Developing Mastery
ACTIVITY: Group Activity Cite one real-life situation that demonstrates polynomial with common monomial factor.
(alert-success) The teacher may elaborate responses of the learners.
G. Finding practical applications of concepts and skills in daily living
Teacher will discuss how factoring applied in real-life situation.
Example: Find the area of a rectangle whose width is $2x – 3$ and the length is $5$ more than the width. Ans. $20{x^2}– 60x + 45$ Let the learners answer.
Ans. $20{x^2} – 60x + 45$
H. Making Generalizations and abstractions about the lesson
Guide Questions for Generalization:
- What is a polynomial? (Expected answer: Polynomial is an expression of one or more algebraic terms.)
- How can we obtain the factors of polynomials using common monomial factor? (Expected answer: through the GCF.)
- What concepts have you learned from factoring that can be applied in your daily living? (answer may vary)
(alert-success)Teacher must correct immediately the wrong response of the learner.
I. Evaluating learning
Individual Work
A. Find the GCF of the following monomials.
1. $a{x^4}$, ${-a^2}{x^6}$, ${a^3}{x^2}$
2. $56{x^2}$, $-4x$, $-12$
3. $ab{x^2}$, $-axz$, $bxy$
B. Factor the following polynomials.
4. $5{y^2}+10$
5. $14{p^2}+21$