GCF What does it stand for? What is it?. What do these have in common??

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