1. Factoring using the
Greatest Common Factor
Module 10 - Topic 1

2. Factors
A factor is a number that divides evenly into
a number.
View this Cool Math website to review
factors. There is only the 1 page to review.

3. Prime Factorization
A Prime number is divisible by 1 and itself.

4. Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
number.

5. Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
number.
Every number has a unique prime factorization.

6. Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
number.
Every number has a unique prime factorization.
Such as the prime factorization of
2 2
A) 36 = 2 ⋅ 2 ⋅ 3 ⋅ 3 or 2 ⋅ 3

7. Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
number.
Every number has a unique prime factorization.
Such as the prime factorization of
2 2
A) 36 = 2 ⋅ 2 ⋅ 3 ⋅ 3 or 2 ⋅ 3
B) 105 = 3 ⋅ 5 ⋅ 7

8. Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
number.
Every number has a unique prime factorization.
Such as the prime factorization of
2 2
A) 36 = 2 ⋅ 2 ⋅ 3 ⋅ 3 or 2 ⋅ 3
B) 105 = 3 ⋅ 5 ⋅ 7
If you do not remember how to find the prime factorization
of a number, Purple Math will help you review Prime
Factorization here.

9. Finding & Factor GCF of a Polynomial
View this 5 minute Prentice Hall video to learn how to find
the GCF of a Polynomial.

10. Finding & Factor GCF of a Polynomial
View this 5 minute Prentice Hall video to learn how to find
the GCF of a Polynomial.

11. Finding & Factor GCF of a Polynomial
View this 5 minute Prentice Hall video to learn how to find
the GCF of a Polynomial.
Now view this Cool Math website to learn how to factor
the GCF from a polynomial.
There are 4 pages to review.
Be sure to do the Try It and Your Turn problems in your
notebook. Check your answers on the following slides.

12. Page 2 Try It
Factor: 2
2x − 4x

13. Page 2 Try It
Factor: 2
2x − 4x
= 2x ⋅ x − 2x ⋅ 2

14. Page 2 Try It
Factor: 2
2x − 4x
= 2x ⋅ x − 2x ⋅ 2

15. Page 2 Try It
Factor: 2
2x − 4x
= 2x ⋅ x − 2x ⋅ 2
= 2x ( x − 2 )

16. Page 2 Try It
Factor: 2
2x − 4x
= 2x ⋅ x − 2x ⋅ 2
= 2x ( x − 2 )

17. Page 2 Try It
Factor: 2
2x − 4x
= 2x ⋅ x − 2x ⋅ 2
= 2x ( x − 2 )

18. Page 2 Try It
Factor: 7x + 14x 2

19. Page 2 Try It
Factor: 7x + 14x 2
= 7x ⋅1 + 7x ⋅ 2x

20. Page 2 Try It
Factor: 7x + 14x 2
= 7x ⋅1 + 7x ⋅ 2x

21. Page 2 Try It
Factor: 7x + 14x 2
= 7x ⋅1 + 7x ⋅ 2x
= 7x (1 + 2x )

22. Page 2 Try It
Factor: 7x + 14x 2
= 7x ⋅1 + 7x ⋅ 2x
= 7x (1 + 2x )

23. Page 2 Try It
Factor: 7x + 14x 2
= 7x ⋅1 + 7x ⋅ 2x
= 7x (1 + 2x )

24. Page 4 Your Turn
Factor: 2 4 3 3 3 5 7
15a b − 5ab + 20a b + 10a b

25. Page 4 Your Turn
Factor: 2 4 3 3 3 5 7
15a b − 5ab + 20a b + 10a b
3 3 3 2 3 4 4
= 5ab ⋅ 3ab − 5ab ⋅1 + 5ab ⋅ 4a + 5ab ⋅ 2a b

26. Page 4 Your Turn
Factor: 2 4 3 3 3 5 7
15a b − 5ab + 20a b + 10a b
3 3 3 2 3 4 4
= 5ab ⋅ 3ab − 5ab ⋅1 + 5ab ⋅ 4a + 5ab ⋅ 2a b

27. Page 4 Your Turn
Factor: 2 4 3 3 3 5 7
15a b − 5ab + 20a b + 10a b
3 3 3 2 3 4 4
= 5ab ⋅ 3ab − 5ab ⋅1 + 5ab ⋅ 4a + 5ab ⋅ 2a b
3
(
= 5ab 3ab − 1 + 4a + 2a b 2 4 4
)

28. Page 4 Your Turn
Factor:
4 3 2 2 5 6
6x y + 2x y − 8x y

29. Page 4 Your Turn
Factor:
4 3 2 2 5 6
6x y + 2x y − 8x y
2 2 2 2 2 2 2 3 4
= 2x y ⋅ 3x y + 2x y ⋅1 − 2x y ⋅ 4x y

30. Page 4 Your Turn
Factor:
4 3 2 2 5 6
6x y + 2x y − 8x y
2 2 2 2 2 2 2 3 4
= 2x y ⋅ 3x y + 2x y ⋅1 − 2x y ⋅ 4x y

31. Page 4 Your Turn
Factor:
4 3 2 2 5 6
6x y + 2x y − 8x y
2 2 2 2 2 2 2 3 4
= 2x y ⋅ 3x y + 2x y ⋅1 − 2x y ⋅ 4x y
2 2
(
= 2x y 3x y + 1 − 4x y 2 3 4
)

32. Factor.
5 3 3 2 2
5x y + 25x y − 15x y

33. Answer: 2
( 3 2
5x y x + 5xy − 3x y 2
)
Here’s how...

34. Answer: 2
( 3
5x y x + 5xy − 3x y 2 2
)
Here’s how...
5 3 3 2 2
5x y + 25x y − 15x y
5
5x y = 5 x x x x x y
3 3
25x y = 5 5 x x x y y y
2 2
−15x y = −1 5 3 x x y y

35. Answer: 2
( 3
5x y x + 5xy − 3x y 2 2
)
Here’s how...
5 3 3 2 2
5x y + 25x y − 15x y
5
5x y = 5 x x x x x y
3 3
25x y = 5 5 x x x y y y
2 2
−15x y = −1 5 3 x x y y
2
GCF: 5x y

36. Answer: 2
( 3
5x y x + 5xy − 3x y 2 2
)
Here’s how...
5 3 3 2 2
5x y + 25x y − 15x y
5
5x y = 5 x x x x x y
3 3
25x y = 5 5 x x x y y y
2 2
−15x y = −1 5 3 x x y y
2
GCF: 5x y

37. Answer: 2
( 3
5x y x + 5xy − 3x y 2 2
)
Here’s how...
5 3 3 2 2
5x y + 25x y − 15x y
5
5x y = 5 x x x x x y
3 3
25x y = 5 5 x x x y y y
2 2
−15x y = −1 5 3 x x y y
2
GCF: 5x y

38. Answer: 2
( 3
5x y x + 5xy − 3x y 2 2
)
Here’s how...
5 3 3 2 2
5x y + 25x y − 15x y
5
5x y = 5 x x x x x y
3 3
25x y = 5 5 x x x y y y
2 2
−15x y = −1 5 3 x x y y
2
GCF: 5x y

39. Factor:
8 3 5 5 8
12d e − 18d e − 27e

40. Answer: 3
( 8 5 2
3e 4d − 6d e − 9e 5
)
Here’s how...

41. Answer: 3
( 8 5 2
3e 4d − 6d e − 9e 5
)
Here’s how...
8 3 5 5 8
12d e − 18d e − 27e
8 3
12d e = 2 2 3 d 5
d 3
e 3
5 5
−18d e = −1 2 3 3 d 5
e 3
e 2
8 3 5
−27e = −1 3 3 3 e e

42. Answer: 3
( 8 5 2
3e 4d − 6d e − 9e 5
)
Here’s how...
8 3 5 5 8
12d e − 18d e − 27e
8 3
12d e = 2 2 3 d 5
d 3
e 3
5 5
−18d e = −1 2 3 3 d 5
e 3
e 2
8 3 5
−27e = −1 3 3 3 e e
3
GCF: 3e

43. Answer: 3
( 8 5 2
3e 4d − 6d e − 9e 5
)
Here’s how...
8 3 5 5 8
12d e − 18d e − 27e
8 3
12d e = 2 2 3 d 5
d 3
e 3
5 5
−18d e = −1 2 3 3 d 5
e 3
e 2
8 3 5
−27e = −1 3 3 3 e e
3
GCF: 3e

44. Answer: 3
( 8 5 2
3e 4d − 6d e − 9e 5
)
Here’s how...
8 3 5 5 8
12d e − 18d e − 27e
8 3
12d e = 2 2 3 d 5
d 3
e 3
5 5
−18d e = −1 2 3 3 d 5
e 3
e 2
8 3 5
−27e = −1 3 3 3 e e
3
GCF: 3e

45. Answer: 3
( 8 5 2
3e 4d − 6d e − 9e 5
)
Here’s how...
8 3 5 5 8
12d e − 18d e − 27e
8 3
12d e = 2 2 3 d 5
d 3
e 3
5 5
−18d e = −1 2 3 3 d 5
e 3
e 2
8 3 5
−27e = −1 3 3 3 e e
3
GCF: 3e

46. Factor:
12 8 5
14a − 28a + 14a

47. Answer: 5
( 7
14a a − 2a + 1 3
)
Here’s how...

48. Answer: 5
(
14a a − 2a + 1 7 3
)
Here’s how...
12 8 5
14a − 28a + 21a
12
14a = 2 7 a 5
a 7
8 5 3
−28a = −1 2 2 7 a a
5 5
21a = 2 7 a

49. Answer: 5
(
14a a − 2a + 1 7 3
)
Here’s how...
12 8 5
14a − 28a + 21a
12
14a = 2 7 a 5
a 7
8 5 3
−28a = −1 2 2 7 a a
5 5
21a = 2 7 a
5
GCF: 14a

50. Answer: 5
(
14a a − 2a + 1 7 3
)
Here’s how...
12 8 5
14a − 28a + 21a
12
14a = 2 7 a 5
a 7
8 5 3
−28a = −1 2 2 7 a a
5 5
21a = 2 7 a
5
GCF: 14a

51. Answer: 5
(
14a a − 2a + 1 7 3
)
Here’s how...
12 8 5
14a − 28a + 21a
12
14a = 2 7 a 5
a 7
8 5 3
−28a = −1 2 2 7 a a
5 5
21a = 2 7 a
5
GCF: 14a

52. Answer: 5
(
14a a − 2a + 1 7 3
)
Here’s how...
12 8 5
14a − 28a + 21a
12
14a = 2 7 a 5
a 7
8 5 3
−28a = −1 2 2 7 a a
5 5
21a = 2 7 a No factors but there is an imaginary 1
5
GCF: 14a

53. Great Job!
You’ve finished reviewing Factoring with a GCF notes.
Exit and proceed to the Mastery Assignment.