Grade 8 Common Monomial Factoring

1. PREPARED BY: SIR CHRISTOPHER M. RAMA
LESSON 1

2. INDIVIDUAL ACTIVITY
Get a piece of paper and a pen.
Do all of the directions given by writing them down
in your paper. There are 16 directions you need to
follow in 2 minutes ONLY so you must hurry!

3. 1. Read all the 16 steps first before doing or
writing anything.
2. Write your surname in the center of your
paper.
3. At the top of your surname, write numbers
1 to 10.
4. Draw three hearts at the top of number 3.
5. Shade the second heart.

4. 6. Encircle all even numbers (2, 4, 6, 8, 10).
7. At the bottom of your paper, write your first
name.
8. Fold your paper in half. (making 2 columns)
9. Open your paper and wave to the teacher.
10.Draw a triangle at the back of your paper.

5. 11.Put an “X” in the center of the triangle.
12.Use the tip of your pen to poke a hole in
your paper straight through the “X” mark.
13.Tap your desk 10 times.
14.Write your teacher’s name anywhere in
the paper.

6. 15.If you have carefully done all steps, say
“I’M DONE!”
16.Now that you have finished reading
everything, do only steps 1 and 2.

7. What does the activity imply?
What might happen if we do not
obey or follow directions?

8. PREPARED BY: SIR CHRISTOPHER M. RAMA
LESSON 1

9. 𝟑𝒙 𝟐 + 𝟏𝟐𝒙
𝒙 𝟐 − 𝟒
𝒙 𝟐 + 𝟔𝒙 + 𝟗
𝒙 𝟑 − 𝟖
𝒙 𝟐 + 𝟓𝒙 + 𝟔
(𝟑𝒙)(𝒙 + 𝟒)
(𝒙 + 𝟐)(𝒙 − 𝟐)
(𝒙 + 𝟑)(𝒙 + 𝟑)
(𝒙 + 𝟐)(𝒙 𝟐 − 𝟐𝒙 + 𝟒)
(𝒙 + 𝟐)(𝒙 + 𝟑)

10. 𝟑𝒙 𝟐 + 𝟏𝟐𝒙
𝒙 𝟐 − 𝟒
𝒙 𝟐 + 𝟔𝒙 + 𝟗
𝒙 𝟑 − 𝟖
𝒙 𝟐
+ 𝟓𝒙 + 𝟔
(𝟑𝒙)(𝒙 + 𝟒)
(𝒙 + 𝟐)(𝒙 − 𝟐)
(𝒙 + 𝟑)(𝒙 + 𝟑)
(𝒙 + 𝟐)(𝒙 𝟐 − 𝟐𝒙 + 𝟒)
(𝒙 + 𝟐)(𝒙 + 𝟑)

11. • Factoring is the process of
finding the factors of an
expression.
• It is the reverse process of
multiplication
Factoring Polynomials

12. 10x2y = ( ? )( ? )
Find the factors which when multiplied,
results to the given polynomial.

13. A. Common Monomial Factoring
B. Difference of Two Squares
C. Perfect Square Trinomial
D. Sum and Difference of Two Cubes
E. Quadratic Trinomial
Factoring Polynomials

17. Greatest Common Factor

18. Find the Greatest Common Factor of 6 and 15.

19. Find the Greatest Common Factor of 6 and 15.
6 15
2 3 3 5
3 is the GCF of 6 and 15.

20. Find the Greatest Common Factor of 12 and 28.

21. Find the Greatest Common Factor of 12 and 28.
12 28
3 4 4 7
4 is the GCF of 12 and 28.

22. Copy the following set of numbers and
expressions. Find the GCF.

23. 15 & 251.

24. 6 & 182.

25. 4 & 43.

26. 8 & 124.

27. 15 & 185.

28. xy & xz6.

29. abs & cbn7.

30. efg & e8.

31. x4 & x39.

32. 2a5 & 6a310.

33. 1.
2.
3.
4.
5.
15 & 25
6 & 18
4 & 4
8 & 12
15 & 18
6
4
4
3
5

34. 6.
7.
8.
9.
10.
xy & xz
abs & cbn
efg & e
x4 & x2
2a5 & 6a3
b
e
x2
2a3
x

35. PREPARED BY: SIR CHRISTOPHER M. RAMA
LESSON 1.1
(CMF)

36. CMF is like splitting an expression into
two factors, obtaining a common factor
from all terms.
ab + ac + ad
Common Monomial Factoring
ab + ac + ad
a (b + c + d)a

37. 1. Find the GCF of the numerical
coefficients; Find the variable with the
least exponent in each term of the
polynomial.
2. Divide each term in the polynomial by
the obtained GCF. The resulting
quotient is the other factor.
Steps in CMF:

38. Factor 12x3y5 – 20x5y2z .
4x3y2GCF:
1. Find the GCF of the numerical coefficients; Find the variable with the least
exponent in each term of the polynomial.
2. Divide each term in the polynomial by the obtained GCF. The resulting
quotient is the other factor.
3y3 – 5x2zQuotient:
4x3y2 (3y3 – 5x2z)Factored Form:

39. Factor 10a2b7 – 25a2b .
5a2bGCF:
1. Find the GCF of the numerical coefficients; Find the variable with the least
exponent in each term of the polynomial.
2. Divide each term in the polynomial by the obtained GCF. The resulting
quotient is the other factor.
2b6 – 5Quotient:
5a2b (2b6 – 5)Factored Form:

40. Factor 18x5 + 6x3 – 2x.
2xGCF:
1. Find the GCF of the numerical coefficients; Find the variable with the least
exponent in each term of the polynomial.
2. Divide each term in the polynomial by the obtained GCF. The resulting
quotient is the other factor.
9x4 + 3x2 – 1Quotient:
2x (9x4 + 3x2 – 1 )Factored Form:

41. Work with a partner.
Factor the following polynomials.
Determine the GCF, Quotient, and
Factored Form

42. 25a6b10 + 15a9b61.
2.
18x5 + 12x3 – 21x3.
14x4 – 21x3 + 7x2

43. 25a6b10 + 15a9b61.
2.
18x5 + 12x3 – 21x3.
14x4 – 21x3 + 7x2
GCF:
Quotient:
Factored Form:
GCF:
Quotient:
Factored Form:
GCF:
Quotient:
Factored Form:
5a6b6
2x2 – 3x + 1
3x

44. 25a6b10 + 15a9b61.
2.
18x5 + 12x3 – 21x3.
14x4 – 21x3 + 7x2
GCF:
Quotient:
Factored Form:
GCF:
Quotient:
Factored Form:
GCF:
Quotient:
Factored Form:
5a6b6
2x2 – 3x + 1
3x
5b4 + 3a3
5a6b6 (5b4 + 3a3)
7x2
7x2 (2x2 – 3x + 1)
(6x4 + 4x2 – 7)
3x (6x4 + 4x2 – 7)

45. Factor the following polynomials.
Determine the GCF, Quotient, Factored Form.
Only the Factored Form will be counted with a
point.

46. 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
10x + 10y + 10z
bx + by + bz
3x³ + 6x² + 9x
10x + 5y –20z
7a³ + 14a² + 21
12a² + 12a
12am + 6a²m
72e + 36f – 27g
5a³ + a³b
5ax + 15ay - 25 az

47. 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
10(x + y + z)
b(x + y + z)
3x(x2 + 2x + 3)
5(2x + y – 4z)
7(a3 + 2a2 + 3)
12a(a + 1)
6am(2 + a)
9(8e + 4f – 3g)
a3(5 + b)
5a(x + 3y – 5z)

48. IDEA FOR GROUP ACTIVITY
• Decode a message by factoring the polynomials.
• The message is the task they have to do.

49. State what you have learned from
today’s Lesson.
• Factoring
• GCF
• CMF
• Steps in CMF
• Following
Directions

50. Factor the following polynomials.
Choose from the given options.

51. 5x + 5y + 5z
5 ( x + y + z )
5x ( x + y + z )
1.

52. ax + ay + az
ayz ( x + y + z )
a ( x + y + z )
2.

53. 4x³ + 8x² + 12x
4x ( x2 + 2x + 3)
4x3 ( 1 + 2x + 3x2 )
3.

54. 6x + 18y – 9z
3 (2x + 6y – 3z)
6 (x + 3y – 3z)
4.

55. 32xy – 18x2
18x ( 2y – x)
2x (16y – 9x )
5.

56. ANSWERS

57. 5x + 5y + 5z
5 ( x + y + z )
5x ( x + y + z )
1.

58. ax + ay + az
ayz ( x + y + z )
a ( x + y + z )
2.

59. 4x³ + 8x² + 12x
4x ( x2 + 2x + 3)
4x3 ( 1 + 2x + 3x2 )
3.

60. 6x + 18y – 9z
3 (2x + 6y – 3z)
6 (x + 3y – 3z)
4.

61. 32xy – 18x2
18x ( 2y – x)
2x (16y – 9x )
5.

62. 2.
3.
4.
5.
1. 5 ( x + y + z )
a ( x + y + z )
4x(x2 +2x+3)
3(2x+6y–3z)
2x (16y – 9x )

63. PASSING SCORE

64. (x + y)(x – y)1.
2.
(y – 9)(y + 9)3.
(a + 4)(a – 4)
4.
(x2 + 10)(x2 – 10)5.
(2x + 3)(2x – 3)
HomeWork:
Multiply the following binomials.