FACTORING TECHNIQUES * Common Monomial Factor (CMF)

1. FACTORING COMMON
MONOMIAL FACTOR
M R . C A R L O J U S T I N O J . L U N A
S e c o n d a r y S c h o o l T e a c h e r I
MATHEMATICS 8
Patterns and Algebra
(1st Quarter)

2. The Mathematician’s Prayer
Heavenly Father, thank You for the blessings
You gave unto us,
Add joy to the world,
Subtract evil from our lives.
Multiply the good things for us.
Divide the gifts and share them to others.
Convert badness to goodness.
Help us raise our needs to You.
Extract the roots of immoralities
and perform our different functions in life.
Tell us all that life is as easy as math.
Help us all to solve our problems.
This we ask in Jesus’ name, the greatest
mathematician who ever lived on earth, Amen.

3. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA 3
WARM UP
Simplify the given
expressions.

4. WARM UP! Simplify the given expressions.
4MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
𝟑𝒂(𝒂 𝟐
− 𝟕𝒂 + 𝟒)
Answer:
𝟑𝒂 𝟑
− 𝟐𝟏𝒂 𝟐
+ 𝟏𝟐𝒂

5. WARM UP! Simplify the given expressions.
5MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
−𝟑𝒂𝒃(𝟔𝒂 𝟐
𝒃 − 𝟐𝒂𝒃 𝟐
)
Answer:
−𝟏𝟖𝒂 𝟑
𝒃 𝟐
+ 𝟔𝒂 𝟐
𝒃 𝟑

6. WARM UP! Simplify the given expressions.
6MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
𝟐𝒙 𝟐
(𝟓𝒙 𝟐
+ 𝟒𝒙 − 𝟏)
Answer:
𝟏𝟎𝒙 𝟒
+ 𝟖𝒙 𝟑
− 𝟐𝒙 𝟐

7. WARM UP! Simplify the given expressions.
7MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
𝟒𝒚 𝟑
(𝟐𝒙𝒚 𝟐
+ 𝒙𝒚 + 𝟐𝒙)
Answer:
𝟖𝒙𝒚 𝟓
+ 𝟒𝒙𝒚 𝟒
+ 𝟖𝒙𝒚 𝟑

8. WARM UP! Simplify the given expressions.
8MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
−𝒂𝒃 𝟐
(𝟑𝒂 𝟐
𝒃 − 𝟓𝒂𝒃)
Answer:
−𝟑𝒂 𝟑 𝒃 𝟑 + 𝟓𝒂 𝟐 𝒃 𝟑

9. FACTORING COMMON
MONOMIAL FACTOR
M R . C A R L O J U S T I N O J . L U N A
S e c o n d a r y S c h o o l T e a c h e r I
MATHEMATICS 8
Patterns and Algebra
(1st Quarter)

10. 10MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
A monomial can be written as a product of its
factors.
Example:
FACTORS
4𝑎2
𝑏5 = 2 ∙ 2 ∙ 𝑎 ∙ 𝑎 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏
8𝑎3
𝑏4 = 2 ∙ 2 ∙ 2 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏
The common factor of 4𝑎2
𝑏5
and 8𝑎3
𝑏4
is
2 ∙ 2 ∙ 𝑎 ∙ 𝑎 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 = 𝟒𝒂 𝟐
𝒃 𝟒

11. 11MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
You can also find the greatest common factor of
two or more polynomials.
Example:
GREATESTCOMMON FACTOR
6𝑥2
𝑦 = 2 ∙ 3 ∙ 𝑥 ∙ 𝑥 ∙ 𝑦
9𝑥𝑦 = 3 ∙ 3 ∙ 𝑥 ∙ 𝑦
The GCF of 6𝑥2
𝑦 and 9𝑥𝑦 is 𝟑𝒙𝒚.

12. 12MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
If the terms of a polynomial
have a common factor, the
polynomial can be written
as a product.
This is called factoring.
FACTORING

13. 13MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
Factor 𝟏𝟎𝒎 − 𝟐𝟓𝒏
𝟏𝟎𝒎 = 𝟓 ∙ 𝟐 ∙ 𝒎
𝟐𝟓𝒏 = 𝟓 ∙ 𝟓 ∙ 𝒏
𝑮𝑪𝑭 = 𝟓
𝟏𝟎𝒎 − 𝟐𝟓𝒏
= 𝟓(𝟐𝒎 − 𝟓𝒏)

14. 14MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
Factor 𝟐𝟏𝒂 𝟐
𝒃 − 𝟑𝟓𝒂𝒃 𝟐
𝟐𝟏𝒂 𝟐
𝒃 = 𝟑 ∙ 𝟕 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃
𝟑𝟓𝒂𝒃 𝟐 = 𝟓 ∙ 𝟕 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃
𝑮𝑪𝑭 = 𝟕 ∙ 𝒂 ∙ 𝒃
𝑮𝑪𝑭 = 𝟕𝒂𝒃

15. 15MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
Factor 𝟐𝟏𝒂 𝟐
𝒃 − 𝟑𝟓𝒂𝒃 𝟐
𝟐𝟏𝒂 𝟐
𝒃 − 𝟑𝟓𝒂𝒃 𝟐
Answer: 𝟕𝒂𝒃(𝟑𝒂 − 𝟓𝒃)

16. 16MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
Factor 𝟏𝟔𝒂 𝟐
𝒃 𝟑
− 𝟐𝟎𝒂 𝟑
𝒃 𝟓
𝟏𝟔𝒂 𝟐
𝒃 𝟑 = 𝟐 ∙ 𝟐 ∙ 𝟐 ∙ 𝟐 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃
𝟐𝟎𝒂 𝟑
𝒃 𝟒 = 𝟐 ∙ 𝟐 ∙ 𝟓 ∙ 𝒂 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃
𝑮𝑪𝑭 = 𝟐 ∙ 𝟐 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃
𝑮𝑪𝑭 = 𝟒𝒂 𝟐
𝒃 𝟑

17. 17MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
Factor 𝟏𝟔𝒂 𝟐
𝒃 𝟑
− 𝟐𝟎𝒂 𝟑
𝒃 𝟓
𝟏𝟔𝒂 𝟐
𝒃 𝟑
− 𝟐𝟎𝒂 𝟑
𝒃 𝟓
Answer: 𝟒𝒂 𝟐
𝒃 𝟑
(𝟒 − 𝟓𝒂𝒃 𝟐
)

18. 18MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
Factor 𝟐𝟖𝒂 𝟑
𝒃 𝟓
+ 𝟑𝟓𝒂 𝟐
𝒃 𝟒
− 𝟏𝟒𝒂𝒃 𝟑
𝟐𝟖𝒂 𝟑
𝒃 𝟓 = 𝟐 ∙ 𝟐 ∙ 𝟕 ∙ 𝒂 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃
𝟑𝟓𝒂 𝟐
𝒃 𝟒 = 𝟓 ∙ 𝟕 ∙ 𝒂 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃
𝑮𝑪𝑭 = 𝟕 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃
𝑮𝑪𝑭 = 𝟕𝒂𝒃 𝟑
𝟏𝟒𝒂𝒃 𝟑 = 𝟐 ∙ 𝟕 ∙ 𝒂 ∙ 𝒃 ∙ 𝒃 ∙ 𝒃

19. 19MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
Factor 𝟐𝟖𝒂 𝟑
𝒃 𝟓
+ 𝟑𝟓𝒂 𝟐
𝒃 𝟒
− 𝟏𝟒𝒂𝒃 𝟑
𝟐𝟖𝒂 𝟑
𝒃 𝟓
+ 𝟑𝟓𝒂 𝟐
𝒃 𝟒
− 𝟏𝟒𝒂𝒃 𝟑
Answer: 𝟕𝒂𝒃 𝟑
(𝟒𝒂 𝟐
𝒃 𝟐
+ 𝟓𝒂𝒃 − 𝟐)

20. 20MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
YOU TRY!
Find the factors of
the given
expressions.

21. 21MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
= 2𝑎 2𝑏 − 5𝑐
EXERCISES
1. 4𝑎𝑏 − 10𝑎𝑐
2. 10𝑎2
+ 15𝑎3
3. 16𝑚3
𝑛2
+ 20𝑚2
𝑛3
4. 21𝑚𝑛4
− 35𝑚2
𝑛2
+ 7𝑚3
𝑛
5. 27𝑥𝑦3 + 81𝑥2 𝑦 − 36𝑥𝑦
= 5𝑎2
2 + 3𝑎
= 4𝑚2
𝑛2
4𝑚 + 5𝑛
= 7𝑚𝑛 3𝑛3
− 5𝑚𝑛 + 𝑚2
= 9𝑥𝑦 3𝑦2
+ 9𝑥 − 4

22. THANK YOU!
22
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) Mr. CARLO JUSTINO J. LUNA
M R . C A R L O J U S T I N O J . L U N A
S e c o n d a r y S c h o o l T e a c h e r I
MATHEMATICS 8
Patterns and Algebra
(1st Quarter)