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What is Tic-Tac-Toe?

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**Tic-Tac-Toe and Factoring**

What is tic-tac-toe? Game with x’s and o’s Method used to factor trinomials (series of steps to help you factor faster) Why use it? When used correctly, it is virtually fool proof It organizes your work Check it after you fill in

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**FIRST TERM INCLUDE SIGN!! MIDDLE TERM INCLUDE SIGN!! LAST TERM**

if subtracting OR the larger factor you the sign of This sign tells Both factors If adding. This sign tells Subtract the You to add or Factors. FIRST TERM INCLUDE SIGN!! MIDDLE TERM INCLUDE SIGN!! LAST TERM

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**Let’s look at the parts of the board.**

This is where it all begins!! Row 1 Then proceed from here. Column 3 Each row will multiply across Each column will factor down!! (almost like a magic square puzzle)

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**First term in first spot. Last term in next spot. **

Row 1 First term in first spot. Last term in next spot. Multiply these two and place the product in the last spot. Column 3 These factors must add or subtract to give you the middle term in the problem. List all the factors of this number, when you find the two numbers that add or subtract to give the middle term, you have the correct factors. Be sure to watch your signs to know whether to add or subtract the factors and to know the signs of the factors you are using.

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**Let’s outline the steps.**

Row 1 – First term in first spot, last term in 2nd spot. Now multiply together and place answer in last spot. Column 3 – Factor the term in the first spot. List all the factors of this number then choose the two that add or subtract (depending on your signs) to give you the middle term in the problem. Row 2 – Spot 2 and 3 have the SAME SIGN. Row 3 – Spot 2 and 3 have the SAME SIGN. Now factor Columns 1 and 2. It doesn’t matter which one you do first. When you have finished, multiply across Row 2 and Row 3. When multiplied together, spot 1 and 2 will always equal spot 3. You can also check yourself by multiplying UP each column since multiplying is opposite of factoring.

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**Place first term in first spot Place last term in next spot **

We will be looking at the factors of “c” that we can add together to get “b” This signs shows Both signs Will be neg This sign tells you to add The factors. Place first term in first spot Place last term in next spot Multiply these two Determine signs that go in blocks Now factor down column 3. List all the factors and choose the ones that will add/subtract to give you the middle term. Next, factor the middle column down. Last, factor the first column down. Check yourself, multiply ACROSS (L to R) all rows and UP all columns to see if you get the correct products. Multi across Multi up Multi up Add/sub To get Middle term Multi across

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**SIGNS!! ax2 + bx – c ax2 + bx + c ax2 - bx - c ax2 - bx + c Both will**

Negative “c” Positive “c” ax2 + bx – c ax2 - bx - c ax2 + bx + c ax2 - bx + c LOOK HERE FIRST!!! Add factors Same Signs Both will Be positive LOOK HERE FIRST!!! Subtract factors Opposite Signs Larger # will Be positive LOOK HERE FIRST!!! Add factors Same Signs Both will Be Negative Larger # will Be Negative LOOK HERE FIRST!!! Subtract factors Opposite Signs

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**To determine your signs**

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**To determine your signs**

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To factor a trinomial of the form: x2 + bx + c

To factor a trinomial of the form: x2 + bx + c

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