1. Factoring Trinomials Using the Tic-Tac-Toe Method
Created by
Kathy Turner

2. X 72x -X -72x 2X 36x -2X -36x 3X 24x -3X -24x 4X 18x -4X -18x 6X 12x
Step 1: Multiply first term 6x2 by the last term 12.
6x2+17x+12
-X -72x
± x ± 72x
2X 36x
± 2x ± 36x
-2X -36x
3X 24x
± 3x ±24x
Step 2: List all factors in the table to the right.
-3X -24x
± 4x ±18x
4X 18x
± 6x ±12x
-4X -18x
±8x ±9x
6X 12x
Step 3: Pick the terms that will equal the middle term in problem.
-6X -12x
8X 9x
-8X -9x

3. Take these 2 GCFs on top and put them in the first parenthesis to double check your answer. Do the same thing for the other two GCFs.
6x2+17x+12
Draw a tic-tac-toe board and place your first and last terms in the board as shown:
GCF 2x
GCF 3
This block
stays blank
First Term
6x2
Pick two table terms that equal the middle term x and place them on the tic-tac-toe table:
Table Term 9x
GCF 3x
Table Term 8x
Last Term 12
GCF 4
Next, find the greatest common factors and place them in the remaining tic-tac-toe squares.
Last, double check your board:
(2x+3)(3x+4) = 6x2+17x+12
6x2+9x+8x+12
6x2+17x+12

4. -2x 15x 2x -15x -3x 10x -30x2 -x 30x x -30x 3x -10x -5x 6x 5x -6x
Step 1: Multiply first term 2x2 by the last term -15.
2x2 + x - 15
-x x
x x
-2x x
Step 2: List all factors in the table to the right.
2x x
-3x x
3x x
Step 3: Pick the terms that will equal the middle term in problem.
-5x times 6x = -30x2
-5x x
5x x

5. 2x2+x-15
You must keep the negative on the –5x because it is on the edge.
Draw a tic-tac-toe board and place your first and last terms in the board as shown:
GCF 2x
GCF -5
This block
stays blank
First Term
2x2
Pick two table terms that equal the middle term x and place them on the tic-tac-toe table:
Table Term
-5x
GCF x
Table Term 6x
Last Term
-15
GCF 3
Next, find the greatest common factors and place them in the remaining tic-tac-toe squares.
Last, double check your board:
(2x-5)(x+3) = 2x2+x-15
2x2-5x+6x-15
2x2+x-15