# Factors completely different types of polynomials (polynomials with common monomial factor)

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Content Standard

The learner demonstrates understanding of key concepts of factors of polynomials (Polynomials with common monomial factor)

Performance Standard

The learner is able to formulate real-life problems involving factors of polynomials (with common monomial factor)

Competency

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
Guide the students to answer the following:

• 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. $(a - b)$

• 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:

1. a
2. c
3. 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:

1. What is a polynomial? (Expected answer: Polynomial is an expression of one or more algebraic terms.)
2.  How can we obtain the factors of polynomials using common monomial factor? (Expected answer: through the GCF.)
3. 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. $14{p^2}+21$