Q&A #104

Teachers' Lounge Discussion: Factoring trinomials

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From: M.J.Bell <mjbell@tenet.edu>
To: Teacher2Teacher Public Discussion
Date: 1998062714:26:12
Subject: Re: ax^3+ bx^2 y + cxy^2 + dy^3 works great with a factor table.

I explained the basic factor table in another message on the public
discussion.  Here is a specific example such as you asked for.
The basic rules of the table are multiply across and multiply down.
The numbers in parentheses indicate the order the box is filled in.

Factor:  2x^3 - 3x^2y + 4xy^2 - 6y^3

   (6)   (7)   (3)         x^2    -3y      -3x^2y
   (8)   (9)   (4)         2x      2y^2     4xy^2
   (1)   (2)   (5)         2x^3   -6y^3    -12x^3y^3

The factors are (box6 + box 9) (box 8 + box 7)  or  

   (x^2 + 2y^2)(2x - 3y)

Box 5 is the checking box.  If it is not the product down and across,
then it will not factor into 2 binomials.  Box 6 is the GCF of box 3
and 1.  Box 1 always contains the first term and box 2 the last.  The
two middle terms are interchangeable in boxes 3 and 4.

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