Tic-Tac-But No Toe In the following tic tac’s there are four numbers Tic-Tac-But No Toe In the following tic tac’s there are four numbers. Find the relationship that the two numbers on the right have with the two numbers on the left. -90 10 1 -9 36 -6 -12 -36 -6 6 -30 -6 -1 5 -49 7 -7 120 30 34 4 -81 9 -9 -24 -6 -10 -4 -72 24 21 -3 16 4 8 -6 -3 -1 2 49 -7 -14 Observations 1. What did you find? 2. Did it follow the pattern every time?

Tic-Tac-But No Toe Use your discoveries from Part 1 to complete the following Tic Tac’s. 9 10 16 -10 18 9 6 7 -35 2 4 -5 45 14 6 -5 -3 -2 -15 2 72 -38 -6 -5 -72 -1 -36 5 -22 9

Find the 2 numbers that complete the Tic Tac. How to Factor Put the equation in standard form: ax2 + bx + c Factor out the GCF, if necessary. Multiply a and c and put the product in the first box. Put b in the third box. ax2 + bx +c Rewrite the polynomial using the two numbers to “break up” the b. Factor by grouping. (a)(c) ? b Find the 2 numbers that complete the Tic Tac.

EXAMPLE x2 – x – 12 -12 ? -1 What 2 numbers complete the Tic Tac? -12 3 -1 -4 Your answer is (x + 3) (x – 4). x2 – x - 12 x2 + 3x – 4x - 12 x(x + 3) – 4(x + 3)

EXAMPLES 5x + 3x2 – 12 *Remember to re-write in standard form 3X2 + 5X - 12 -36 ? 5 What 2 numbers complete the Tic Tac? Your answer is (x + 3) (3x – 4). 3x2 + 5x - 12 3x2 + 9x – 4x - 12 3x(x + 3) – 4(x + 3) -36 9 5 -4

EXAMPLES 2X2 + 8X - 64 *Remember that sometimes a GCF should be factored out before beginning. 2(X2 + 4X – 32) -32 ? 4 What 2 numbers complete the Tic Tac? Your answer is 2[(x + 8) (x – 4)]. 2(x2 + 4x – 32) 2(x2 + 8x – 4x – 32) 2[x(x + 8) – 4(x + 8)] -32 8 4 -4