GREATEST COMMON FACTOR

Definition of factors Factors are terms that are multiplied. The factors of 5 are 1 and 5. The prime factors of 6 are 2 and 3. ( The smallest prime number is 2) All of the factors of 6 are 1, 2, 3, and 6. All of the factors of a4 are 1, a, a2, a3, a4

What is factoring? Factoring is just backwards distributing. Distributing: 5( x + 2 ) = 5x + 10 When you are factoring, they give you the answer and you have to come up with the question. Factoring: 5x + 10 = 5( x + 2 )

Pulling out a common factor When you pull a term out in front of the parentheses you want to be sure: It is a factor of each original term. It’s the BIGGEST common factor of the terms.

Let’s try some examples Factor 2a6 + 4a2 Biggest factor of both 2 and 4? 2 Biggest factor of both a6 and a2? a2 Common factor: 2a2 ‘Leftovers’ : ( a4 + 2 ) Answer: 2a2( a4 + 2 ) Distribute to check your work! 2a2( a4 + 2 ) = 2a6 + 4a2

Let’s try some examples Factor 2a6b4c8 + 4a2b5c9 + 6a3b3c7 What’s the biggest factor of 2, 4 and 6? 2 What’s the biggest factor of a6, a2, and a3? a2 What’s the biggest factor of b4, b5, and b3? b3 What’s the biggest factor of c8, c9, and c7? c7 2a2b3c7( a4bc + 2b2c2 + 3a )

Watch those signs! Factor 2x – 4y Factor – 3x – 6y -3( x + 2y ) I had to make it a +2y or we wouldn’t get the right answer when we distribute to check.

WHENEVER YOU FACTOR ALWAYS pull out the biggest common factor FIRST!