1. Greatest Common Factor
Chapter 6 Lesson 1
Greatest Common Factor

2. Greatest Common Factor
What do you think this means?

3. Often abbreviated as: GCF
Definition
Greatest Common Factor:
the largest monomial that divides (is a factor of) each term of the polynomial.
Often abbreviated as: GCF

4. Let’s compare! Left: Best friend, Wes.
Right: Your teacher, Mr. Stillwell.
Looking at these two pictures, what do Wes and Mr. Stillwell have in COMMON?
Red Helmets
Caucasian
Glasses
Outside
Male

5. Greatest Common Factor!
We compared the two pictures….
Greatest Common Factor is the same!
Find everything each term (of a polynomial) have in common!

6. Find GCF (greatest common factor)
To find the GCF, there are 5 steps to follow:
What do we know about the polynomial?
How many terms?
Monomial, Binomial or Trinomial?

7. 2. What must we find?
Largest number that divides into each coefficient (Factor tree)
Largest variable that divides into each coefficient (smallest exponent)

8. 3. Calculate the GCF by multiplying the constant and variable you found in step #2.

9. 4. Rewrite our polynomial with the GCF.

10. 5. Check our answer!

11. Step by Step…
Use the 5 step method to find the greatest common factor of the following polynomial: 3x3 + 6x2 – 12x

12. 3x3 + 6x2 – 12x Trinomial Variables: x3, x2, and x
1. What do we know?
Trinomial
Variables: x3, x2, and x
Coefficients: 3, 6, and -12

13. 3x3 + 6x2 – 12x Largest number that evenly divides each coefficient 3
What must we find?
Largest number that evenly divides each coefficient 3
Largest variable that evenly divides each term. X

14. 3x3 + 6x2 – 12x 3 * X = 3X 3. Calculate GCF:
Largest number that divides each term

15. 3x3 + 6x2 – 12x 3 * X = 3X 3. Calculate GCF:
Largest variable that divides each term

16. 3x3 + 6x2 – 12x
3. Calculate GCF: 3 * X = 3X
GCF

17. 3x3 + 6x2 – 12x
4. Rewrite our polynomial
3x(x2 +2x – 4)
GCF
Factor

18. 3x3 + 6x2 – 12x
5. Check our answer. Multiply GCF through parenthesis: 3x(x2 +2x – 4) = 3x3 + 6x2 – 12x
THEY MATCH!!

19. Is this important? Used for simplification in later use
Assists with graphing in later use
Finding similarities of objects (as previously discussed)

20. Quick Review
GCF: Greatest monomial that is a factor of each term of a polynomial.
5 steps: Know, Find, Calculate, Rewrite, Check (KFC & RC)