1. 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?

2. 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

3. 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.

4. 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)

5. 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

6. 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