Factoring by Grouping - Grid Box MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts

If you are trying to use factoring by grouping and are having difficulties keeping the signs correct, you may want to try this grid method for writing out the steps.

 This grid box method ONLY works if you have factored out any common factors BEFORE beginning the grid process! (If you do not factor out common factors first, you will get a wrong answer.)

This grid box approach starts the same way as the factoring by grouping. The only difference is the way your results are going to be displayed.

 Example of Factoring by Grouping with a Grid Box:

Factor: 8x2 + 26x + 15
There are no common factors in these three terms, so we are ready to go to the grid box method.

1. Find a • c.
a • c = 8 • 15 = 120
2. Find two new factors of a • c (120) that add up to b (+26).
20 • 6 = 120
20 + 6 = 26
3. Prepare a grid box (4 cells). Place the leading term in the upper left cell, and the constant term in the lower right cell.
 8x2 + 15
4. Just like in the original factoring by grouping, create the "middle" terms using the two new factors. Be careful of the signs. Order is not important when placing these new "middle" terms. Either arrangement will work.
 8x2 20x 6x + 15
5. Now, find a common factor in each ROW of the box and write it outside of the box to the right (or left) of each row.
4x
 8x2 20x 6x + 15
+3
6. Now, find the common factor in each COLUMN of the box and write it outside of the box above (or below) each column.
2x
+5
4x
 8x2 20x 6x + 15
+3
7. Read off the answers from the edges of the grid box.
(4x + 3)(2x + 5)

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