1. 4-4: (GCF) Greatest Common Factor And 4-3 review of Factoring

2. What you will learn…  To find prime factorizations of monomials.  To find the greatest common factors of monomials. … and why.  In order to build toward factoring greater polynomials.

3. Factoring Monomials Factoring is the reverse of multiplying. To factor means to break down an expression into a product of two or more expressions called factorizations. Ex. (4x)(5x) = 20x 2 20x 2 = (4x)(5x) Multiplying Factoring Ex. 2(10x 2 ) = 20x 2 20x 2 = 2(10x 2 ) (2x)(10x) = 20x 2 20x 2 = (2x)(10x) x(20x) = 20x 2 20x 2 = x(20x) (-4x)(-5x) = 20x 2 20x 2 = (-4x)(-5x) Many ways to multiply and end with a product of 20x 2 Many ways to factor 20x 2

4. Factoring Completely Factoring completely (finding the Prime Factorization) means breaking down a product or whole number into a product of prime numbers (numbers that cannot be broken down any further). Factoring Completely can be done using a Factor Tree… Ex. Factor each monomial completely. 50g 2 h 2 25 5 2 5 5 g g h

5. Factoring Completely Factoring completely (finding the Prime Factorization) means breaking down a product or whole number into a product of prime numbers (numbers that cannot be broken down any further). Factoring Completely can be done using a Factor Tree… Ex. Factor each monomial completely. –49a 3 b 2 –1 49 7 –1 7 7 a a a b b

6. Factoring Completely Factoring Completely can be done using a Factor Tree… Ex. Factor each monomial completely. 14m 2 n 2 7 m m n 27a 2 b 2 3 3 3 a a b b 70rs 2 2 5 7 r s s

7. Factoring Completely Factoring Completely can be done using a Factor Tree… Ex. Factor each monomial completely. 66d 4 2 3 11 d d d d –30c 2 d –1 2 3 5 c c d 243n 2 3 3 3 3 3 n n

8. Finding the GCF The GCF (greatest common factor) means finding the greatest number that can “go into” two or more numbers. Finding the GCF can be found by breaking down numbers into their prime factorization and finding which factors they share… Ex. Find the GCF of each set of monomials. 2772 In other words, what is the biggest number that can go into both 27 and 72?? 3 3 32 2 2 3 3 Since they both share (3 3) their GCF is equal to 9 Determine what both prime factorizations share…

9. Finding the GCF Finding the GCF can be found by breaking down numbers into their prime factorization and finding which factors they share… Ex. Find the GCF of each set of monomials. 24d 2 30c 2 d In other words, what is the biggest number that can go into both 24d 2 and 30c 2 d?? 2 2 2 3 d d2 3 5 c c d They both share 2 3 d so their GCF is 6d Determine what both prime factorizations share… Greatest Common Factor

10. Finding the GCF Finding the GCF can be found by breaking down numbers into their prime factorization and finding which factors they share… Ex. Find the GCF of each set of monomials. 42a 2 b 6a 5 18a 3 GCF is 6a 2 Determine what both prime factorizations share… Greatest Common Factor

11. Finding the GCF Finding the GCF can be found by breaking down numbers into their prime factorization and finding which factors they share… Ex. Find the GCF of each set of monomials. 28a 2 b 2 63a 3 b 2 91b 3 GCF is 7b 2 Determine what both prime factorizations share… Greatest Common Factor