# 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

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:

1. What is/are the picture?
2. What have you observed on the picture?
3. Did you find any common?

### 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”

### 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. $(a-b)$

1. What are the prime factors of each term?
2. What is the common factor?
3. 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.

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

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.

Note: 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. $20{x^2} – 60x + 45$

### 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?

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. $14{p^2} + 21$