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 ) = 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 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 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 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 ) 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!