GREATEST COMMON FACTOR Definition of factors Factors are

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GREATEST COMMON FACTOR

GREATEST COMMON FACTOR

Definition of factors Factors are terms that are multiplied. The factors of 5 are

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 a 4 are 1, a, a 2, a 3, a 4

What is factoring? Factoring is just backwards distributing. Distributing: 5( x + 2 )

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

Pulling out a common factor When you pull a term out in front of

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 2 a 6 + 4 a 2 Biggest factor

Let’s try some examples Factor 2 a 6 + 4 a 2 Biggest factor of both 2 and 4? 2 Biggest factor of both a 6 and a 2? a 2 Common factor: 2 a 2 ‘Leftovers’ : ( a 4 + 2 ) Answer: 2 a 2( a 4 + 2 ) Distribute to check your work! 2 a 2( a 4 + 2 ) = 2 a 6 + 4 a 2

Let’s try some examples Factor 2 a 6 b 4 c 8 + 4

Let’s try some examples Factor 2 a 6 b 4 c 8 + 4 a 2 b 5 c 9 + 6 a 3 b 3 c 7 What’s the biggest factor of 2, 4 and 6? 2 What’s the biggest factor of a 6, a 2, and a 3? a 2 What’s the biggest factor of b 4, b 5, and b 3? b 3 What’s the biggest factor of c 8, c 9, and c 7? c 7 2 a 2 b 3 c 7( a 4 bc + 2 b 2 c 2 + 3 a )

Watch those signs! Factor 2 x – 4 y 2( x – 2 y

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

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

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