2Tic-Tac-Toe and Factoring What is tic-tac-toe?Game with x’s and o’sMethod used to factor trinomials (series of steps to help you factor faster)Why use it?When used correctly, it is virtually fool proofIt organizes your workCheck it after you fill in
3FIRST TERM INCLUDE SIGN!! MIDDLE TERM INCLUDE SIGN!! LAST TERM if subtracting ORthe larger factoryou the sign ofThis sign tellsBoth factorsIf adding.This sign tellsSubtract theYou to add orFactors.FIRST TERMINCLUDE SIGN!!MIDDLE TERMINCLUDE SIGN!!LAST TERM
4Let’s look at the parts of the board. This is where it all begins!!Row 1Then proceed from here.Column 3Each row will multiply acrossEach column will factor down!!(almost like a magic square puzzle)
5First term in first spot. Last term in next spot. Row 1First term in first spot.Last term in next spot.Multiply these two and place the product in the last spot.Column 3These 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.
6Let’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.
7Place 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 showsBoth signsWill be negThis sign tellsyou to addThe factors.Place first term in first spotPlace last term in next spotMultiply these twoDetermine signs that go in blocksNow 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 acrossMulti upMulti upAdd/subTo getMiddletermMulti across
8SIGNS!! ax2 + bx – c ax2 + bx + c ax2 - bx - c ax2 - bx + c Both will Negative“c”Positive“c”ax2 + bx – cax2 - bx - cax2 + bx + cax2 - bx + cLOOK HEREFIRST!!!Add factorsSameSignsBoth willBepositiveLOOK HEREFIRST!!!Subtract factorsOppositeSignsLarger # willBepositiveLOOK HEREFIRST!!!Add factorsSameSignsBoth willBeNegativeLarger # willBeNegativeLOOK HEREFIRST!!!Subtract factorsOppositeSigns