The document is a lesson plan on factoring polynomials for a quarter 1 mathematics class, covering the greatest common factor (GCF) and the definition of polynomials. It includes examples and exercises to illustrate how to determine the GCF through prime factorization and how to factor polynomials into simpler forms. Additionally, it emphasizes the process of factoring as the reverse of polynomial multiplication.

1. Quarter 1
MATHEMATICS 8
Mrs. Anne R. Rabino-Mesana

2. Factoring Polynomials
a. G- Greatest
C- Common
M- Monomial
F- Factor
Quarter 1: Lesson 1

3. Observe…
What is common in the given pictures?

4. Observe…
What is common in the given pictures?

5. What is common in:
2, 4, 6

6. Factors of 2, 4 and
6
2-
4-
6-
1, 2
1, 2, 4
1, 2, 3,
6
What is their common factor aside from 1?

7. Observe
x, 2x, 3x, 4x

8. Greatest Common
Factor (GCF)

9. Ways of finding the GCF: Prime Factorization
GrEAtEst COMMON FACTOR (GCF)
Example: Find the GCF of 8 and 12
8 =2 ∙ 2 ∙ 2
12= 2 ∙ 2 ∙ 3
GCF=

10. 1. 16 and 48
Example
Find the GCF of:
2. 15 and 21
3. 24 and 36

11. What is the GCF of ?
GrEAtEst COMMON FACTOR (GCF)
Answer:
What is the GCF of ?
Answer:

12. The word “POLYNOMIAL”
comes from Latin Greek words:
Poly (many) and Nomen
(name or term)
POLYNOMIAL
According to the Compact Oxford English Dictionary

13. -An algebraic expression that shows a
sum/difference of two or more terms
containing whole number exponents
on the variable.
POLYNOMIAL
According to the Compact Oxford English Dictionary

14. A variable is a symbol which
represents an unknown
value.
VARIABLE

15. A symbol or a number with
a fixed value.
CONSTANTS

16. EXAMPLE OF POLYNOMIAL
𝟒 𝒙 𝟐
− 𝟐
This is a polynomial since the variables
have no negative (all positive)
exponents.

17. EXAMPLE OF POLYNOMIAL
𝟒 𝒙 𝟐
− 𝟐
How many terms do we have?
Numerical
Coefficient
Literal
Coefficient
Exponent
Constant

18. GCF: NUMERICAL COEFFICIENTS WITH
LITERAL COEFFICIENTS
4 𝑥3
𝑎𝑛𝑑 8 𝑥 2
𝑮𝑪𝑭=𝟐∙𝟐∙ 𝒙∙ 𝒙𝒐𝒓 𝟒 𝒙𝟐
4 𝑥3
=2 ∙ 2 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥
8 𝑥 2
=2 ∙ 2 ∙ 2 ∙ 𝑥 ∙ 𝑥

19. 1.
Example
Find the GCF of:
2.
3.

20. Is used to find the Greatest Common
Factor of the given pair of monomials.
PRIME FACTORIZATION

21. 4.
Find the GCF
5.
1. 2 𝑎𝑛𝑑 10
3. ,
2 . 48 𝑎𝑛𝑑 18

22. Greatest Common
Monomial Factor
Factoring

23. Example
𝟔 𝒙+ 𝟑 𝒙𝟐
Factor the
Polynomial
GCMF=
GCMF Other Factor
𝟑 𝒙 (𝟐+𝒙)
Factored Form

24. Example
𝟒 𝒂𝟐
+𝟗 𝒃𝟐
Factor the
Polynomial
GCMF Other Factor
Factored Form

25. Example
𝟏𝟐 𝒙𝟑
𝒚𝟓
−𝟐𝟎 𝒙𝟓
𝒚𝟐
𝒛
Factor the
Polynomial
GCMF Other Factor
Factored Form

26. Is often called as the reverse
process of multiplying polynomials,
where we write a polynomial as a
product of two or more simpler
polynomials
FACTORING

27. Exercises:
𝟕 𝒑𝟐
− 𝟕 𝒑
Factor the
Polynomial
GCMF Other Factor
Factored Form

28. Exercises:
𝟏𝟖 𝒙𝒚 +𝟑 𝒚
Factor the
Polynomial
GCMF Other Factor
Factored Form

29. QUIZ:
𝟑 𝒎𝟑
− 𝟖 𝒏𝟐
Factor the
Polynomial
GCMF Other Factor
Factored Form

30. QUIZ:
𝟐𝟎 𝒙 𝟓
−𝟑𝟒 𝒙𝟐
Factor the
Polynomial
GCMF Other Factor
Factored Form

31. QUIZ:
𝟏𝟓𝒎𝟑
−𝟏𝟓𝒎𝟐
+𝟐𝟎𝒎
Factor the
Polynomial
GCMF Other Factor
Factored Form

32. Let us have a great school year together!

33. QUIZ: Complete the table
Polynomial GCMF Other
Factor
Factored
Form