What is Tic-Tac-Toe?What is Tic-Tac-Toe?

What is tic-tac-What is tic-tac-toe?toe?

Game with x’s and Game with x’s and o’so’s

Method used to Method used to factor trinomials factor trinomials (series of steps to (series of steps to help you factor help you factor faster)faster)

Why use it?Why use it? When used When used

correctly, it is correctly, it is virtually fool proofvirtually fool proof

It organizes your It organizes your workwork

Check it after you Check it after you fill in fill in

2ax bx c

FIRS

T T

ER

M

LAS

T T

ER

MIN

CLU

DE S

IGN

!!

MID

DLE

TER

MIN

CLU

DE S

IGN

!!

Th

is sign

tells

You

to a

dd

or

Su

btra

ct the

Facto

rs.

Th

is sign te

lls you th

e sig

n o

f th

e la

rger fa

ctor

if subtra

cting

OR

Both

facto

rs If a

dd

ing.

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

This is where it all begins!!

Then proceed from here.

Each row will multiply across

Each column will factor down!!

(almost like a magic square puzzle)

2ax bx c Row 1Row 1

First term in first spot.First term in first spot. Last term in next spot.Last term in next spot. Multiply these two and Multiply these two and

place the product in the place the product in the last spotlast spot..

2 2 3x x 2x 3 23x

Column 3Column 3 These factors must add These factors must add

or subtract to give you or subtract to give you the middle term in the the middle term in the problem. List all the problem. List all the factors of this number, factors of this number, when you find the two when you find the two numbers that add or numbers that add or subtract to give the subtract to give the middle term, you have middle term, you have the correct factors.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.

2x

Let’s outline the steps.Let’s outline the steps. Row 1 – First term in first spot, last term in 2Row 1 – First term in first spot, last term in 2ndnd

spot. Now multiply together and place answer in spot. Now multiply together and place answer in last spot.last spot.

Column 3 – Factor the term in the first spot. List Column 3 – Factor the term in the first spot. List all the factors of this number then choose the two all the factors of this number then choose the two that add or subtract (depending on your signs) to that add or subtract (depending on your signs) to give you the middle term in the problem.give you the middle term in the problem.

Row 2 – Spot 2 and 3 have the SAME SIGN.Row 2 – Spot 2 and 3 have the SAME SIGN. Row 3 – 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 Now factor Columns 1 and 2. It doesn’t matter

which one you do first. When you have finished, which one you do first. When you have finished, multiply across Row 2 and Row 3. When multiply across Row 2 and Row 3. When multiplied together, spot 1 and 2 will always multiplied together, spot 1 and 2 will always equal spot 3.equal spot 3.

You can also check yourself by multiplying UP You can also check yourself by multiplying UP each column since multiplying is opposite of each column since multiplying is opposite of factoring.factoring.

2ax bx c

1st

term

• 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.

3

term

rd 1 *3

Multi

st rd

answer

2

nd

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.

We will be looking at the factors of “c” that we can add together to get “b”

This sign tells you to add

The factors.This

signs s

hows

Both signs

Will

be neg

Multi across

Multi across

Multi u

p

Multi u

p

Add/subTo getMiddleterm

SIGNS!!SIGNS!!

axax2 2 + bx + c+ bx + c

axax2 2 - bx + c- bx + c

axax2 2 + bx – c+ bx – c

axax2 2 - bx - c- bx - c

Positive

“c”

LOOK HEREFIRST!!!

Add factorsSameSigns

Both willBe

positive

LOOK HEREFIRST!!!

Add factorsSameSigns

Both willBe

Negative

LOOK HEREFIRST!!!

Subtract factors

OppositeSigns

Larger # willBe

positive

Larger # willBe

Negative

Negative“c”

LOOK HEREFIRST!!!

Subtract factors

OppositeSigns

“c” is pos.You will ADD

Factors.

x2-bx+c“b” is neg

both factors willbe neg.

x2+bx+c“b” is pos.

both factors willbe pos.

“c” is neg.You will

SUBTRACTFactors.

x2-bx-c“b” is neg

LARGER factor will be neg.

x2+bx-c“b” is pos.

LARGER factorwill be pos.

2 2 3x x 2 7 12x x