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A Final Overview

RULE # 4:

If it has three terms and the coefficient on the squared guy is not a 1...

Make your list and start hammering!

Example:

6x^2 - 19x - 7

First: 1 * 6 and 2 * 3 , Last: 1 * 7 and 7 * 1
 

We need a -19...
 

1) 1 * 6 and 1 * 7 gives 6 and 7 ... no

2) 1 * 6 and 7 * 1 gives 42 and 1 ... no

3) 2 * 3 and 1 * 7 gives 3 and 14 ... no

4) 2 * 3 and 7 * 1 gives 21 and 2 ... -21 + 2 = -19

First: 2 * 3 and Last: 7 * 1 gives ( 2x - 7 ) ( 3x + 1 ) ... the inner terms give -21x and the outer terms give 2x

So,

6x^2 - 19x - 7 = ( 2x - 7 ) ( 3x + 1 )

Example:

                    3x^2- 9x - 12  RULE # 1!!

= 3 ( x^2 - 3x - 4 ) ... now, it's just a NIKE factor... = 3 ( x + 1 ) ( x - 4 )