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

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(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:

  1. What is/are the picture?
  2. What have you observed on the picture?
  3. 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:

  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. $20{x^2} – 60x + 45$

Let the learners answer. 

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. $14{p^2} + 21$                  


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