Old Dogs, New Tricks

I learned a new way to factor trinomials today, so I guess you can teach an old dog new tricks. I am actually rather pleased with myself.

The Algebra kids are learning factoring which, the way I and people much younger than I learned it, involves a lot of guesswork and playing with which factors go where. Now factoring is something that I actually got in math, but the guesswork did sometimes get annoying. Guesswork for kids who have IEPs is torture. They like to have patterns. That's where the new method comes in.

Let’s say your problem, following the model of ax2+bx+c, is to factor 2y2+7y+3.

The first thing you do is multiply the a and c terms. In this case, 2×3=6.

You have to look for factors of six that will add up to the middle term, which in this case is seven. In this instance, the right set of factors is obvious: one and six.

6 1+6=7
1, 6  

Then you make two sets of factoring parentheses like you normally would with this kind of problem. In the first set, you put the first term of the trinomial:

(2y2+ ).

In the second parenthesis, you put the last term of the trinomial:

( + 3 ).

Now you have to add in the factors of six, the two and the three. The way you decide what factor goes where is that you put the ones which have a factor in common together. So….the six goes in the parenthesis with the three, and the one goes in the parenthesis with the two. You have to put them in as 6y and 1y (so you can add them up to 7y). Then your problem looks like this:

(2y2+1y) (6y+3).

Next you factor out what you can from the parentheses:

y (2y+1) 3 (2y+1). See how you factored out the same quantity, (2y+1)? That is part of your answer. Finally, you take the outside terms and put them together for the other parenthesis: (y+3). So your factored trinomial is (2y+3) (y+1).

I hope that make sense to you. It does to me, finally, although I think I am more comfortable with the old way of guessing. It never hurts to learn new things, though. And besides, when it comes to teaching kids with learning disabilities, it is better to have lots of strategies.





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