A powerpoint of Common Monomial Factor based on New DepED Module Standard

1. Factoring : Common
Monomial Factor
Lorie Jane L. Letada
Module 1

2. Objectives
At the end of this lesson, you are expected to:
• identify the greatest common
factor of the given expression,
• factor the polynomial by
common monomial factor.

3. History
Factorization was first
considered by ancient Greek
mathematicians in the case of integers.
They proved the fundamental theorem
of arithmetic, which asserts that every
positive integer may be factored into a
product of prime numbers, which
cannot be further factored into
integers greater than 1.

4. What’s New
Observe the example in the table below.
The lists above are the factors of
36 and 40. How do you factor
integers?

5. Another way of writing the factors of 36 & 40 is by
using a Venn diagram.
Questions:
1. What have you noticed with the
intersection of the two circles?
2. In relation to #1, what do you call
these numbers?
3. What is the GCF of 36 and 40?
4. How do you get the GCF of a given
number?

6. What is it
What is factoring?
Factoring is the process of finding the factors
of an expression. It is also the reverse of
multiplication. It can be factored into a product of
prime numbers.

7. The first technique in factoring polynomial is the Common Monomial
Factor.
Greatest Common Monomial Factor
is the product of the greatest common
factor of the coefficients and the greatest common
factors of the variables.

8. Example 1 Factor 3x + 3y
Step 1. Find the GCF of each
term.
3x = 3 • x
3y = 3 • y
GCF = 3
Step 2.
Divide each term by
the greatest common
factor (GCF): 3
3𝑥
3
= 𝑥
3𝑦
3
= 𝑦
Step 3. Factor out the GCF.
(3)(x) + (3)(y) = 3 ( x + y )

9. Example 2 Factor 2𝑥3
− 6𝑥2
Step 1. Find the GCF of each
term.
2𝑥3
= 2 •x •
6𝑥2
= 3 •
GCF = 2
Step 2.
Divide each term by
the greatest common
factor (GCF): 2𝑥2
2𝑥3
2𝑥2
= 𝑥
6𝑥2
2𝑥2
= 3
Step 3. Factor out the GCF.
(2𝑥2)(x) - (2𝑥2)(3) = 2𝑥2 ( x - 3 )
x • x
2 •x • x
• x • x
2𝑥2
GCF =

10. Activity 1 WHAT’S COMMON?
Directions: Factor the following polynomials by factoring out the common monomial
factor. Write your answer in the corresponding column. The first one is done for you.

11. What I need to remember
• Factoring is the process of finding the factors of an expression.
It is also the reverse of multiplication. It can be factored into a
product of prime numbers.
• Greatest Common Monomial Factor is the product of the
greatest common factor of the coefficients and the greatest
common factors of the variables.