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Unformatted text preview: ing what we multiplied to get the given quantity. We do this all the time
with numbers. For instance, here are a variety of ways to factor 12. 12 = ( 2 ) ( 6 ) 12 = ( 3) ( 4 ) 12 = ( 2 ) ( 2 ) ( 3) æ1ö
12 = ç ÷ ( 24 )
è2ø 12 = ( -2 )( -6 ) 12 = ( -2 )( 2 )( -3) There are many more possible ways to factor 12, but these are representative of many of them.
A common method of factoring numbers is to completely factor the number into positive prime
factors. A prime number is a number whose only positive factors are 1 and itself. For example
2, 3, 5, and 7 are all examples of prime numbers. Examples of numbers that aren’t prime are 4, 6,
and 12 to pick a few.
If we completely factor a number into positive prime factors there will only be one way of doing
it. That is the reason for factoring things in this way. For our example above with 12 the
complete factorization is, 12 = ( 2 ) ( 2 ) ( 3) Factoring polynomials is done in pretty much the same manner. We determine all the terms that
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- Spring '12