1. GCF What does it stand for? What is it?

2. What do these have in common??

4. The greatest common factor (GCF) of two natural numbers is the largest number that is a factor of both numbers. Example: 84 = 2 x 2 x 3 x 7 100 = 2 x 2 x 5 x 5 GCF = 2 x 2 = 4

5. Find the GCF of 84 and 180. 84 = 2 x 2 x 3 x 7 180 = 2 x 2 x 3 x 3 x 5 GCF = 2 x 2 x 3 = 12

6. Find the GCF of 21 and 10. 21 = 3 x 7 10 = 2 x 5 GCF = 1 If two integers have no common prime factors, their GCF is 1. Such numbers are said to be relatively prime.

7. GCF with Variables Note: With variables, the GCF will always be the smallest exponent of a common variable Examples: 12x 3 and 16x 2 45a 5, 50a 7 GCF = 4x 2 GCF = 5a 5

8. What is the greatest common factor?? 5a 35

9. What is the greatest common factor?? 3y -8xy

10. What is the greatest common factor?? 22x 2 -11x Note: With negatives, go by the leading term!!

11. What is the greatest common factor?? -4x 6 -x 4 -2x 2 -x 2 Note: With negatives, go by the leading term!!

12. Factoring = Write the polynomial as a product. STEPS: 1) Find the GCF of all its terms. 2) Write the polynomial as a product by factoring out the GCF from all the terms. - This is done by dividing the original terms of the polynomial by the GCF. 3) The remaining factors in each term will form a polynomial. FACTORING POLYNOMIALS

13. What is the GCF? Example 1 4x + 6y 2 Factor out the GCF 2(2x + 3y)

14. What is the GCF? Example 2 6x 3 – 9x 2 + 12x 3x Factor out the GCF 3x(2x 2 – 3x + 4)

15. 1.16x 2 – 8x You try: Factor What is their GCF? = 8x( ) 2x – 1 2. 2a 3 – 6a = 2a( ) a2a2 – 3

16. 3. 2h 2 k + 2k Factor What is their GCF? = 2k( ) h2h2 + 1 4. 6uv + 9v 2 = 3v( ) 2u + 3v

17. Homework pg. 417 #4 to 50 even