## Wednesday, March 27, 2013

### Factoring Trinomials (A not 1) - The Unconventional Way

My Algebra 2's today were dealing with factoring (4 different ways). This is typically an Algebra 1 skill but we place it in Algebra 2. We deal with GCF, Difference of Squares, and the two types of Trinomials. Last semester, I found a really funky way of factoring trinomials and this semester, I finally put a story behind the method.

The story goes as follows. We start by always looking for a greatest common factor as he gets carried on to the final answer. (He doesn't deal with the shenanigans that are to follow). Then, the evil King Trin kidnaps the new A coefficient and hides him away in the C value. This has now disguised our trinomial as a trinomial where A is 1. This is then easy to factor by looking for a value that multiplies to be C but adds to be B. After this trinomial has been factored, we come to the rescue with the A being placed back next to his x. However, there is an impostor in our midst. To find the impostor, we take the GCF of each parentheses. The impostor is then revealed and he is banished from the kingdom. The leftover factors then rejoice and rejoin with their original GCF. They then live happily every after <3.

The kids had some fun with this story as I was told all day long that it was not nice to kidnap values and then make them go poof. When the impostors are banished, a few kids claim that they are stabbed but I just say they are forced to go away.

This can be a fun method and an easy one too especially if the original A value is not so nice :)

1. This sounds like a very interesting way to teach factoring of trinomials....usually what I do in this cas is teach students how to do "slide and divide"

1. That sounds very smoooooooth :)

2. How do you explain "poof" Algebraically?

1. "poof" is more so the abbreviation the kids come up with when they have taken the GCF from each of the factors in order to find the "imposter" in the story. it's more or less the ability to divide and be left with 1.

3. I have only two concerns about "slide and divide": one, that students often forget the "divide" part, and two, the proof is complicated and rarely explained.

Let me know what you think of this method, which is the reverse of FOILing (so call it deFOILING maybe?), so the students can connect to that familiar process and recognize its analogous relationship to a similarly reversible process, multiplication/division.

2x² - 17x + 36
2x² - 8x - 9x + 36
2x(x - 4) - 9(x - 4)
(x -4)(2x - 9)

The first step is to multiply the leading coefficient and the constant and then find the factors of the result that sum to the middle term's coefficient.
Next, split the middle term into these two factors and rewrite the original polynomial.
The third and final step also involves a familiar process, GCFing, factoring the x - 4 out of both terms.

I like this because you can easily set this next to FOILing (x -4)(2x - 9) and see they are the same.

Feedback is welcome.

Jim

4. I forgot to mention another advantage to this deFOILING method: in addition to reinforcing practice in FOILING and GFCing, it does the same for Grouping for 4-term polynomials.

1. I was about to say! I know that many teachers have taught this method because it does a great job teaching students how to group! I always encourage my kids to go out and find a way that works for them (i learned about this method from one of my kids during the first semester). Factoring is always such a tricky topic for kids that's why I added a story to the slide and divide method. My biggest problem with slide and divide is that it doesn't incorporate taking the GCF first. I harp on this to no end as always always always being the first step when factoring. That's why I essentially removed the notion of divide and said find the fake gcf in the parenthesis as he is the impostor.

I'm thinking that this year, I want to have the kids illustrate this factoring method with a story :)

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