Factoring TrinomialsUsing the Tic-Tac-Toe Method

Created byKathy Turner

Step 1: Multiply first term 6x2 by the last term 12.

6x2+17x+12

72x2

± x ± 72x

± 2x ± 36x

± 3x ±24x ± 4x ±18x

± 6x ±12x

±8x ±9x

Step 2: List all factors in the table to the right.

Step 3: Pick the terms that will equal the middle term in problem.

-3X -24x

-X -72x

2X 36x

3X 24x

X 72x

-4X -18x

6X 12x

4X 18x

-2X -36x

-6X -12x

8X 9x

-8X -9x

Draw a tic-tac-toe board and place your first and last terms in the board as shown:

Last Term12

First Term

6x2Pick two table terms

that equal the middle term x and place them on the tic-tac-toe table:

Table Term9x

Table Term8x

Next, find the greatest common factors and place them in the remaining tic-tac-toe squares.

GCF

4

GCF

3x

GCF

2xGCF

3This blockstays blank

Last, double check your board:

(2x+3)(3x+4) = 6x2+17x+126x2+9x+8x+126x2+17x+12

6x2+17x+12Take 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.

Step 1: Multiply first term 2x2 by the last term -15.

2x2 + x - 15

-30x2

-x 30x x -30x

-2x 15x 2x -15x

-3x 10x 3x -10x

-5x 6x

5x -6x

Step 2: List all factors in the table to the right.

Step 3: Pick the terms that will equal the middle term in problem.

-5x times 6x = -30x2

Draw a tic-tac-toe board and place your first and last terms in the board as shown:

Last Term-15

First Term2x2

Pick two table terms that equal the middle term x and place them on the tic-tac-toe table:

Table Term-5x

Table Term6x

Next, find the greatest common factors and place them in the remaining tic-tac-toe squares.

GCF

3

GCF

x

GCF

2xGCF

-5This blockstays blank

Last, double check your board:

2x2-5x+6x-15

(2x-5)(x+3) = 2x2+x-15

2x2+x-15

2x2+x-15You must keep the negative

on the –5x because it is on

the edge.