From: Claudia (for Teacher2Teacher Service)
Date: Jun 02, 1998 at 21:53:47
Subject: Re: Factoring trinomials

Actually, the most effective way I have found is to use the 
TIC-TAC-TOE method. 

Create a 9 square board.

     a---c---ac    Row one takes the a coefficient in square 1, c in the second  
                   square and the product ac in the third.

                   Next do column 3. What do you multiply to get ac but add to 
                   equal "b"? (Note that we haven't used b yet). Place those 
                   factors along column 3 in rows 2 and 3.

                   Let me take you through an example:  6x^2-7x-3
    6   -3   -18   What multiplies to equal -18 and adds to equal = -7 ?
                   -9 and +2.  Put them in position.

    6   -3   -18
              -9
               2  (Either order is fine.) Now, what are two factors of -9, 
                   such that one divides evenly into the 6 located in row 1 and 
                   the other into the -3, also in row 1?  
                   3 and -3.  Position them.

    6   -3   -18
    3   -3    -9   You can repeat the same thing for factors of 2 or just
    2    1     2   divide the 3 into 6 and get 2, -3 into -3 and get +1.   

                   Now look at the square in the lower left  
    3   -3
    2    1         The diagonals of these form the factored trinomial 
                   (3x+1)(2x-3).

It is somewhat difficult to illustrate this on the computer... I hope this 
makes sense!

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