This document provides a lesson on factoring polynomials. It defines factoring as the reverse process of multiplying polynomials, where a polynomial is written as a product of simpler polynomials. It gives examples of finding the greatest common factor (GCF) of monomials and polynomials using prime factorization. It demonstrates factoring out the GCF to group like terms. Students are provided exercises to practice finding the GCF of pairs of monomials and polynomials.

2. What is common in the given pictures?
2
LESSON 1: FACTORING POLYNOMIALS

3. 3
LESSON 1: FACTORING POLYNOMIALS

4. 4
LESSON 1: FACTORING POLYNOMIALS
What is common in the given pictures?

5. 5
LESSON 1: FACTORING POLYNOMIALS

6. 6
LESSON 1: FACTORING POLYNOMIALS
8, 16, 24
All numbers are divisible by 8

7. 7
LESSON 1: FACTORING POLYNOMIALS
Factors of 2, 4 and 6
2 = 1, 2,
4 = 1, 2, 4,
6 = 1, 2, 3, 6
All have a factor of 2.

8. 8
LESSON 1: FACTORING POLYNOMIALS
x 2x 3x 4x
All these have variable x.
The common factor is x.

9. 9
LESSON 1: FACTORING POLYNOMIALS
We all find
commonalities in
Algebra.

10. 10
LESSON 1: FACTORING POLYNOMIALS
One way to find the
Greatest Common Factor
of two or more numbers
is Prime Factorization.

11. 11
LESSON 1: FACTORING POLYNOMIALS
GCF of 8 and 12

12. 12
LESSON 1: FACTORING POLYNOMIALS
GCF of 8 and 12
8 = 2 · 2 ·2
12 = 2 · 2 · 3
GCF = 2 · 2 = 4

13. 13
LESSON 1: FACTORING POLYNOMIALS
GCF
n3, n5, n6, n9

14. 14
LESSON 1: FACTORING POLYNOMIALS
nk =
k times
n · n · n . . . n · n

15. 15
LESSON 1: FACTORING POLYNOMIALS
GCF
n3, n5, n6, n9

16. 16
LESSON 1: FACTORING POLYNOMIALS
n3 = n · n · n
n5 = n · n · n · n · n · n
n6 = n · n · n · n · n · n
n9 = n · n · n · n · n · n · n · n · n
GCF = n · n · n = n3

17. 17
LESSON 1: FACTORING POLYNOMIALS

18. 18
LESSON 1: FACTORING POLYNOMIALS
A. -4x0 + 1 C. x +
3
4𝑥
B. x + 4y D. 4m3 – 2abc

19. 19
LESSON 1: FACTORING POLYNOMIALS
C. x +
1
4𝑥
Is not a polynomial because the exponent
of the variable x in
1
4𝑥
is -1 which is not a
whole number.
1
4𝑥
= 4𝑥−1

20. 20
LESSON 1: FACTORING POLYNOMIALS

21. 21
LESSON 1: FACTORING POLYNOMIALS
4x2 - 3
Numeral
Coefficient
Constant
Exponent
Literal
Coefficient

22. 22
LESSON 1: FACTORING POLYNOMIALS
4x3 and 8x2
What is the greatest common factor of

23. 23
LESSON 1: FACTORING POLYNOMIALS
4x3 = 2 · 2 · x · x · x
8x5 = 2 · 2 · 2 · 2 · x · x
GCF: 2 · 2 · x · x = 4x

24. 24
LESSON 1: FACTORING POLYNOMIALS
4a3 and 9b2
Factor out the following polynomial:
4a3 =
9b2 =
2 · 2 a · a · a
3 · 3 b · b
GCF =
· 1
· 1
1 Relatively Prime

25. 25
LESSON 1: FACTORING POLYNOMIALS
4a3 and 9b2
What is the greatest common factor of
4a3 =
9b2 =
2 · 2 a · a · a
3 · 3 b · b
GCF =
· 1
· 1
1 Relatively Prime

26. 26
LESSON 1: FACTORING POLYNOMIALS
How about if we get the
GREATEST COMMON FACTOR
of three polynomials?

27. 27
LESSON 1: FACTORING POLYNOMIALS
6a2b2, 3a2b and 15a3b2
What is the greatest common factor of
6a2b2 =
3a2b =
3 · 2 · a · a b · b
3 · a · a b
GCF = 3 · a ·a · b =
15a3b2 = 3 · 5 · a · a · a b · b
· · · ·
3a2b

28. 28
LESSON 1: FACTORING POLYNOMIALS
EXERCISE
GET THE GCF

29. 29
LESSON 1: FACTORING POLYNOMIALS
12a 18abc
6a

30. 30
LESSON 1: FACTORING POLYNOMIALS
4x3y5 12x2y4z3
4x2y4
8x2y4

31. 31
LESSON 1: FACTORING POLYNOMIALS
𝟏
𝟒𝟖
mn2
𝟏
𝟕𝟐
m2n
𝟏
𝟏𝟐
𝒎𝒏
𝟏
𝟏𝟐
𝐦n4

32. 32
LESSON 1: FACTORING POLYNOMIALS
Prime Factorization is used to
find the greatest common factor
of the given pairs of monomials.

33. 33
LESSON 1: FACTORING POLYNOMIALS

34. 34
LESSON 1: FACTORING POLYNOMIALS
FACTORING
often called the reverse process of
multiplying polynomials, where we
write a polynomial as a product of two
or more simpler polynomials

35. 35
LESSON 1: FACTORING POLYNOMIALS