Q&A #104

Teachers' Lounge Discussion: Factoring trinomials

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From: M.J.Bell

To: Teacher2Teacher Public Discussion
Date: 1998062613:44:02
Subject: Factor Table

I was delighted to see your "tic tac toe" method of factoring trinomials. It is very similar to a method I devised several years ago that I called a factor table. I have taught this at some conferences and found it extremely useful in the classroom. I think that it might be a little easier to follow than the tic tac toe, but it is also difficult to explain in this format. I start with a 3 x 3 table as before with one extra box on top. I'll try to explain the table here. The 3 by 3 part of the table always involves multiplication. Multiply across and multiply down. The d cell is the result of adding the c and g cells. Thus the basic rule for the students to remember is mult. across, mult. down and add up. d a b c e f g h i j 1. Put the first term of the trinomial in cell h. 2. Put the last term in cell i. 3. Put the middle term in cell d. 4. Multiply h and i to find j. I call this the checking box. 5. Look for the c and g cells. I call these the "key cells". Their product is in j and their sum is in d. They are interchangeable. 6. Although you now have a choice, I suggest that the next cell is a. It should be the GCF of c and h. 7. The other cells are now easy to figure out. 8. The factors are in the diagonals of a b e f Example: Factor 6x^2 + 5x - 4 5x 2x 4 8x (key) 3x -1 -3x (key) 6x^2 -4 -24x^2 The factors are (2x - 1) and (3x + 4) The table can be checked at a glance by multiplying across, multiplying down, and adding up the two key cells. This also works well for factoring 4 terms that can only be down be grouping. Use the 2 middle terms for the key numbers and their is no need for an addition box. Example: Factor: 2x^3 - 3x^2 + 4x - 6 x^2 -3 -3x^2 2x 2 4x 2x^3 -6 -12x^3 The factors are (x^2 + 2) (2x - 3)

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