GCF What does it stand for? What is it?

What do these have in common??

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 = 2 x 2 x 5 x 5 GCF = 2 x 2 = 4

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

Find the GCF of 21 and = 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.

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

What is the greatest common factor?? 5a 35

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

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

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

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

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

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

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

3. 2h 2 k + 2k Factor What is their GCF? = 2k( ) h2h uv + 9v 2 = 3v( ) 2u + 3v

Homework pg. 417 #4 to 50 even