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Published byMarilynn Golden Modified about 1 year ago

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

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Step 1: Multiply first term 6x 2 by the last term 12. 6x 2 +17x+12 72x 2 ± 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

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

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Step 1: Multiply first term 2x 2 by the last term -15. 2x 2 + x - 15 -30x 2 -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 = -30x 2

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

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