Math A Creative Factoring of Trinomials

Looking for a creative way to encourage students to factor trinomials?  Consider the following process. Please direct questions on this process to Vivian Donnelly.

When teaching students to factor   ax²+bx+c,
consider using the following method:

1.  The first step is to set up the following:  

2.  Find two factors of ac that have a sum of b.

3.  Call these factors f 1 and f 2.  Place them as shown: 

4.  Check to see if there is anything that can be factored out of the
     parentheses in each of the 2 sets.

5.  Reduce the fraction, if possible.

Example:

Factor:

step 1: 

step 2:   find two factors of ac with a sum of b
              find two factors of (24)(6)=144 with a sum of 25 --> 16 & 9

step 3:   

step 4:  factor each set of parentheses
              (24x + 16 ) = 8( 3x + 2)    and    (24x + 9) = 3(8x + 3)

              which means you have

step 5:  reduce if possible.
              this leaves you with ( 3x + 2 )( 8x + 3 )