1. Factoring
GCF and Trinomials

2. Greatest Common Factor
The Greatest Common Factor is the
largest number that will divide into a
group of numbers
Examples:
6, 9
15, 55
GCF = 3
GCF = 5

3. 3. What is the greatest common factor??36 24
The number 12

4. GCF with Variables Note: With variables, the GCF will
Always be the smallest exponent of a
Common variable
Examples:
12x3, 16x2
45a5, 50a7
GCF = 4x2
GCF = 5a5

5. 6. What is the greatest common factor??
The GCF is 5a

6. What is the greatest common factor??
7. 3y -8xy y
11x
8. 22x – 11x
-x2
9. -4x6 - x4 - 2x2

7. Factoring means to write as a product
Always look for a Greatest Common Factor 1st.
Factor 4x + 6y
What is their greatest common factor?
= 2( ) 2x
+ 3y
Lets check.
=2(2x+3y)
= 4x+6y

8. = y( ) 3 – 8x = 2a( ) a2 – 3b2 Factor 11. 3y – 8xy 12. 2a3 – 6ab2
What is their GCF?
= y( ) 3
– 8x
12. 2a3 – 6ab2
= 2a( ) a2
– 3b2

9. = 2k( ) h2 + 1 = 3v( ) 2u + 3v Factor 13. 2h2k + 2k 14. 6uv + 9v2
What is their GCF?
= 2k( ) h2
+ 1
14. 6uv + 9v2
= 3v( ) 2u
+ 3v

10. What if there is not GCF? 3x + 2 Then it is prime x2 + 3x + 2
Unless it is a trinomial, then I have to use another method.

11. GCF Factor: xy – 5y What is common? Answer: y(x - 5)
What if we change the expression slightly?
x(x + 4) – 5(x + 4)
Answer: (x + 4)(x – 5 )

12. GCF
Try these:
3x2 – 6x – 15x3
16x2 – 8x
y(y – 6) + 9(y – 6)