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**Factoring Trinomials Using the Tic-Tac-Toe Method**

Created by Kathy Turner

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**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

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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

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**-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

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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

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4.4 Factoring Quadratic Expressions P216-220. Factoring : Writing an expression as a product of its factors. Greatest common factor (GCF): Common factor.

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