Post on 16-Dec-2015
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.