Q&A #18119

Teachers' Lounge Discussion: "Bottoms up" as a method to factor trinomials

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From: Matt

To: Teacher2Teacher Public Discussion
Date: 2011012011:57:32
Subject: Name

I believe the name comes from when students are asked to use this
method to FACTOR rather than finish solving.
For example:
Factor 2x^2 + 5x + 3...  

In this method we mutiply the "a" term by the "c" term.  The result is
the new "c" value, and we assume "a" to now be 1.

I call this a "cheat". 
(As an educational note, I make then draw an arc from "a" to "c" so
they remember they "cheated" and don't forget to "undo" this later.)

we then factor x^2 + 5x + 6
(x + 3)(x + 2)

Here we "undo our cheat" by dividing each number by the original "a"
(which = 2).

(x + 3/2)(x + 2/2)

Reduce if possible:
(x + 3/2)(x + 1)

Here, I tell my students if in the reduced state we still have
fractions, we bring its "bottom" (denominator) "up" in front of the
variable as its coefficient.

So (2x + 3)(x + 1) are the factors of 2x^2 + 5x + 3.

Hence the name... or so I believe.

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