~~(toc) Table of Contents~~

**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

Learner’s Module (LM) in Math 9, pp. 30 – 32

Intermediate Algebra p.45

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

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 pictures
- 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? (answers may vary)

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)

Note: 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. $2ab + 2ac – 2a$

Ans. $2a$

2. $20{x^2} – 12$

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. ${x^3}{y^2} +x{y^3} + 2{x^2}{y^3}$ |
$x{y^2}({x^2} + y + 2xy)$ |

2. ${x^3} + {x^2}y + x{y^2}$ |
$3({y^2} – 5y – 4) $ |

3. $3{y^2} – 15y – 12$ |
$xy({x^2} + x + y)$ |

### F. Developing Mastery

**ACTIVITY: Group Activity**

Cite one real-life situation that demonstrates polynomial with common monomial factor.

*Note: The teacher may elaborate responses of the learners.*

### G. Finding practical applications of concepts and skills in daily living

### 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)*

*Note: Teacher must correct immediately the wrong response of the learner.*

### I. Evaluating learning

Individual Work

Instructions:

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. $ab{x^2}, - axz,bxy$

Factor the following polynomials.

4. $5{y^2} + 10$

5. $14{p^2} + 21$