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
A) 36 = 2 ! 2 ! 3 ! 3 or 2 ! 3 2 2

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
A) 36 = 2 ! 2 ! 3 ! 3 or 2 ! 3 2 2
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
A) 36 = 2 ! 2 ! 3 ! 3 or 2 ! 3 2 2
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.
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.

11. Page 2 Try It
Factor: 2x ! 4x
2

12. Page 2 Try It
Factor: 2x ! 4x
2
= 2x ! x " 2x ! 2

13. Page 2 Try It
Factor: 2x ! 4x
2
= 2x ! x " 2x ! 2

14. Page 2 Try It
Factor: 2x ! 4x
2
= 2x ! x " 2x ! 2
= 2x ( x ! 2 )

15. Page 2 Try It
Factor: 2x ! 4x
2
= 2x ! x " 2x ! 2
= 2x ( x ! 2 )

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

17. Page 2 Try It
Factor: 7x + 14x 2
= 7x !1 + 7x ! 2x

18. Page 2 Try It
Factor: 7x + 14x 2
= 7x !1 + 7x ! 2x

19. Page 2 Try It
Factor: 7x + 14x 2
= 7x !1 + 7x ! 2x
= 7x (1 + 2x )

20. Page 2 Try It
Factor: 7x + 14x 2
= 7x !1 + 7x ! 2x
= 7x (1 + 2x )

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

22. Page 4 Your Turn
Factor:
15a b ! 5ab + 20a b + 10a b
2 4 3 3 3 5 7
= 5ab ! 3ab " 5ab !1 + 5ab ! 4a + 5ab ! 2a b
3 3 3 2 3 4 4

23. Page 4 Your Turn
Factor:
15a b ! 5ab + 20a b + 10a b
2 4 3 3 3 5 7
= 5ab ! 3ab " 5ab !1 + 5ab ! 4a + 5ab ! 2a b
3 3 3 2 3 4 4

24. Page 4 Your Turn
Factor:
15a b ! 5ab + 20a b + 10a b
2 4 3 3 3 5 7
= 5ab ! 3ab " 5ab !1 + 5ab ! 4a + 5ab ! 2a b
3 3 3 2 3 4 4
3
(
= 5ab 3ab ! 1 + 4a + 2a b 2 4 4
)

25. Page 4 Your Turn
Factor:
6x y + 2x y ! 8x y
4 3 2 2 5 6

26. Page 4 Your Turn
Factor:
6x y + 2x y ! 8x y
4 3 2 2 5 6
= 2x y ! 3x y + 2x y !1 " 2x y ! 4x y
2 2 2 2 2 2 2 3 4

27. Page 4 Your Turn
Factor:
6x y + 2x y ! 8x y
4 3 2 2 5 6
= 2x y ! 3x y + 2x y !1 " 2x y ! 4x y
2 2 2 2 2 2 2 3 4

28. Page 4 Your Turn
Factor:
6x y + 2x y ! 8x y
4 3 2 2 5 6
= 2x y ! 3x y + 2x y !1 " 2x y ! 4x y
2 2 2 2 2 2 2 3 4
2 2
(
= 2x y 3x y + 1 ! 4x y 2 3 4
)

29. Factor.
5x y + 25x y ! 15x y
5 3 3 2 2

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

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

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

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

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

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

36. Factor:
12d e ! 18d e ! 27e
8 3 5 5 8

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

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

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

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

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

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

43. Factor:
14a ! 28a + 14a
12 8 5

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

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

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

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

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

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

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