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GCFWhat does it stand
for? What is it?
What do these have in common??
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 7
100 = 2 x 2 x 5 x 5
GCF = 2 x 2 = 4
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
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.
GCF with VariablesNote: With variables, the GCF willalways be the smallest exponent of acommon variable
Examples:12x3 and 16x2
45a5, 50a7
GCF = 4x2
GCF = 5a5
What is the greatest common factor??
5a 35
What is the greatest common factor??
3y -8xy
What is the greatest common factor??
22x2
-11x
Note: With negatives, go by the leading term!!
What is the greatest common factor??
-4x6-x4-2x2
-x2
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
6x3 – 9x2 + 12x
3x
Factor out the GCF 3x(2x2 – 3x + 4)
1. 16x2 – 8xYou try: Factor
What is their GCF?
= 8x( ) 2x
– 1
2. 2a3 – 6a= 2a( )a2 – 3
3. 2h2k + 2kFactor
What is their GCF?
= 2k( )h2+ 1
4. 6uv + 9v2
= 3v( )2u
+ 3v
Homework
pg. 417 #4 to 50 even
Homework
pg. 417 #4 to 50 even