Transcript What is Tic-Tac-Toe?

What is Tic-Tac-Toe?
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What is tic-tactoe?
Game with x’s and o’s
Method used to factor
trinomials (series of
steps to help you
factor faster)
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Why use it?
When used correctly,
it is virtually fool
proof
It organizes your
work
Check it after you fill
in
This sign tells
You to add or
Subtract the
Factors.
This sign tells
you the sign of
the larger factor
if subtracting OR
Both factors
If adding.
 bx  c
ax
2
LAST TERM
INCLUDE SIGN!!
MIDDLE TERM
INCLUDE SIGN!!
FIRST TERM
Let’s look at the parts of the 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)
ax  bx  c
2
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x  2x  3
2
x
2
3 3x
2
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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.
2x
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.
Let’s outline the steps.
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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.
We will be
looking at
the factors
of “c” that
we can
add
together
to get “b”
ax  bx  c
2
• Place first term in first spot
This sign tells
• Place
you to
add last term in next spot
The factors.
• Multiply these two
•Determine signs that go in blocks
Multi
1st
term
3rd
term

Multi across
Multi up
Multi up

Multi across
• Now factor down column 3. List all the
factors and choose the ones that will
add/subtract to give you the middle term.
1st *3rd
answer


Add/sub
To get
Middle
term
 2nd
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.
SIGNS!!
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ax2 + bx + c
Both will
Be
positive
 ax2
LOOK
HERE
FIRST!!!
Add
factors
Same
Signs
- bx + c
Both will
Be
Negative
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Larger #
will
Be
positive
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LOOK
HERE
FIRST!!!
Add
factors
Same
Signs
ax2 + bx – c
LOOK HERE
FIRST!!!
Subtract
factors
Opposite
Signs
ax2 - bx - c
Larger #
will
Be
Negative
LOOK HERE
FIRST!!!
Subtract
factors
Opposite
Signs
“c” is pos.
You will ADD
Factors.
x2-bx+c
“b” is neg
both factors will
be neg.
x2+bx+c
“b” is pos.
both factors will
be pos.
“c” is neg.
You will
SUBTRACT
Factors.
x2-bx-c
“b” is neg
LARGER factor
will be neg.
x2+bx-c
“b” is pos.
LARGER factor
will be pos.
x  2x  3
2
x  7 x  12
2