Most of you may know that teaching students how to factor trinomials is a hair raising experience. Well, I learned a new way a couple of years ago and it made my life a lot easier. I don't remember who created this method but it has worked for me and I believe it will work for you.
Example 3x(squared)+ 10x -8
step 1 Have students multiply the first coefficient with the constant
3 times 8 = 24 (notice no signs were used)
step 2 Have students find all the factors or 24
1 times 24
2 times 12
3 times 8
4 times 6
Now have them respond to the question...which of these factor
do you subtract to get the middle coefficient of 10.
You used subtract becasue the last term asks you to
subtract 8.
Hopefully your students will respond 2 and 12.
step 3 Now ask students if the second term will be acquired if you
a) subtract 12 from 2 (2 - 12)
b) subtract 2 from 12 (12 - 2)
step 4 Now using write the following ( x ) (x )
and then include the two numbers found in step 3: +12 and -2. and
it doesn't matter where they are placed making sure why you used -2.
(x + 12) (x - 2)
step 5 Now make sure you explain to your students that
x times x is x(squared) but our origial expression had a 3 in front
and that 12 times -2 is -24 and not -8 as the original.
(Almost done)
step 6 Now you will explain to your students that since there was a leading
coefficient of 3, we need to bring it back to our factors by
dividing the constants by the leading coefficient.
(x + 12/3) (x -2/3) And ask if the 12/3 can be reduced and the
2/3 can be reduced to lowest terms. 12/3 = 4 but 2/3 gives 0.6666
step 7 Now we are in the finishing stages. Rewrite step 6 to look like
(x + 4) (x - 2/3) and complete the last factor by bring the
denominator as the leading coefficient of x.
(x + 4) (3x - 2) your solution and ask them to check.