The document provides instructions on factoring polynomials by identifying and using the greatest common factor (GCF). It includes examples and exercises to help learners practice factoring polynomials completely and demonstrates the steps involved in this process. The lesson emphasizes the importance of expressing terms as products of prime factors and rewriting polynomials in their factored form.

1. Direction: Express the following
numbers as prime factors.
1) 2 • 2 • 3
2) 2 • 3 • 3
3) 2 •2 •2 •5
4) 2 •2•3• 3• 𝑎• a•b
5) 2•2•5• x• 𝑥 • x• y • y • z • z • z • z

2. Give the GCF of the following sets
of numbers/ expressions
1) 2, 4, 6, 8
Answer
2
2) 3, 6, 9,12 3
3) 20g, 30h, 40i, 50j 10
4) 2a2
b, 3a2
c, 6a2
d, 12a2
b a2
5) 6ad,18bd,12cd,24de 6d
Answer

3. Lesson 1:
In this lesson, the learner is able to factor
polynomials with Common Monomial Factor.(M8ALla-b-
1)

4. Factoring is the reverse process of multiplication. It means to
rewrite or express the number/ expression as a product of two or more
numbers/ expressions.
Note: Polynomials are algebraic expressions whose variables have
positive integral exponents.
A monomial is a polynomial with only one term.
Things to Process

5. 1. If the polynomial is equal to , then is called?
A. factor B. GCF C. product D. multiplier
Illustrative Examples
Step 1: Express each term of the polynomial as prime factors.
Step 3: Divide each term of the polynomial by the GCF.
Step 4:Rewrite the polynomial in factored form.
The complete factored form of is .
𝟔 𝒙+𝟑
𝟑(𝟐 𝒙+𝟏)
𝟑 𝟑
Step 2: Determine the GCF.
GCF: 3
Solution:
¿𝟐 𝒙 +𝟏

6. Factor each polynomial completely.
Example 1:
Solution:
Step 1: What is the GCF of the
numerical coefficients in each term?
Step 2: Divide each term of
the polynomial by the GCF
Step 3:Rewrite the polynomial
in factored form
Do we have similar result to the complete factorization
method?
2x +1
Write the
GCF here
𝟑(𝟐 𝒙+𝟏)
6x +3
3

7. Decomposition
Complete
Factorization

8. 5 𝑥
5 𝑥
5 𝑥
¿𝟔 𝒙𝟐
+ 𝒙 −𝟓
2. What is the GCF of
A. B. C. D.
Illustrative Examples
Step 3: Divide each term of the
polynomial by the GCF
Step 4:Rewrite the polynomial in factored form
The complete factored form of is .
30 𝑥3
+5 𝑥2
−25 𝑥
𝟓 𝒙 (𝟔 𝒙𝟐
+𝒙 −𝟓)
Step 1: Express each term of the
polynomial as prime factors.
Step 2: Determine the GCF.
Solution:
GCF: 5x

9. Factor each polynomial completely.
Example 2:
Solution:
Step 2: Divide each term of
the polynomial by the GCF
Step 3:Rewrite the polynomial
in factored form
Do we have similar result to the complete factorization
method?
𝟔 𝒙𝟐
−𝟓
Write the
GCF here
𝟓 𝒙 (𝟔 𝒙𝟐
+𝒙 −𝟓)
𝟑𝟎 𝒙𝟑
−𝟐𝟓𝒙
𝟓 𝒙
+𝟓 𝒙𝟐
Step 1: In each term:
- What is the GCF of the numerical
coefficients?
- What is the common variable with
the least exponent?
+𝒙

10. Decomposition
Complete
Factorization

11. 6 𝑥2
+9 𝑥
3 𝑥 3 𝑥
3. What are the factors of ?
A. B. C. D.
Illustrative Examples
Step 3: Divide each term of the polynomial by
the GCF
Step 4:Rewrite the polynomial in factored form
The complete factored form of is.
𝟑 𝒙(𝟐 𝒙+𝟑)
Step 1: Express each term of the
polynomial as prime factors.
Step 2: Determine the GCF.
Solution:
GCF: 3x
¿2 𝑥+3

12. Factor each polynomial completely.
Example 3:
Solution:
Step 1: In each term:
- What is the GCF of the numerical
coefficients?
- What is the common variable with
the least exponent?
Step 2: Divide each term of
the polynomial by the GCF
Step 3:Rewrite the polynomial
in factored form
Do we have similar result to the complete factorization
method?
𝟐 𝒙 +𝟑
Write the
GCF here
𝟑 𝒙(𝟐 𝒙+𝟑)
𝟔 𝒙𝟐
+𝟗 𝒙
𝟑 𝒙

13. Complete
Factorization
Decomposition

14. In the two methods, which one is more
convenient to use? Why?

15. Practice exercise
4. What should be multiplied to to get ?
A. C.
B. D.
5. The area of a rectangle is . One dimension is . What is the other dimension?
A. C.
B. D.
Using any method, kindly show the solution for number 4 and 5.

16. Practice exercise
4. What should be multiplied to to get ?
A. C.
B. D.
Step 2: Divide each term of
the polynomial by the GCF
Step 3:Rewrite the polynomial
in factored form
𝒙𝟐
𝒚𝟐
Write the
GCF here 𝟗 𝒚
𝟒 𝒙𝟐
𝒚 (𝒙𝟐
𝒚𝟐
+𝟑𝒙 −𝟗 𝒚)
𝟒 𝒙𝟒
𝒚𝟑
−𝟑𝟔𝒙𝟐
𝒚𝟐
4 𝑥2
𝑦
+𝟏𝟐 𝒙𝟑
𝒚
Step 1: In each term:
- What is the GCF of the numerical
coefficients?
- What is the common variable with
the least exponent?
+𝟑 𝒙

17. Developing Mastery
Factor each polynomial completely.
1.) 4.)
2.) 5.
3.)
𝑨𝒏𝒔𝒘𝒆𝒓 :𝟑(𝟏𝟎𝒙−𝟑)
𝑨𝒏𝒔𝒘𝒆𝒓 :𝟏𝟐𝒃(𝒂+𝟐𝒄+𝟑𝒂𝒄) 𝑨𝒏𝒔𝒘𝒆𝒓 : 𝟏𝟐 𝒎𝟑
𝒏 ¿
𝑨𝒏𝒔𝒘𝒆𝒓 :𝟑 𝒙(𝟗𝒙 𝒚𝟑
−𝟓 𝒙+𝟔𝒘𝟒
)

18. To factor polynomials with Common Monomial Factor:
• determine the GCF of the terms in the polynomial
• divide each term of the polynomial by the GCF
• rewrite the polynomial as a product of the common factor and the
remaining factor
Things to Ponder