The document discusses factoring polynomials using the greatest common factor (GCF). It provides examples of factoring different polynomials and finding their prime factorizations. It includes step-by-step workings to show how to factor terms with the GCF and distribute factors. The document aims to teach readers how to factor polynomials down to their simplest form.

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.