Factorization Methods and Factor Tables in Mathematics
T
IC
-T
AC
-T
OE
F
ACTORING
Presented by:
Jennifer Morgan and Christina Guynes
Grady ISD
Kermit ISD
D
AY
O
NE
– F
ACTOR
T
ABLES
Find the pair of numbers that will multiply to
make the bottom number and add to give you the
top number.
3
4
4
6
5
4
F
ACTOR
T
ABLES
…
3
-8
-4
-21
36
4
-7
4
T
IC
-T
AC
-T
OE
M
ETHOD
2
3
6
6
1
1
1
2
3
x
x
First term
goes here
Third term
goes here
Multiply
across to get
this number
What factors
of 6 will add
to get 7?
Factors must multiply
across to last number
Factors multiply up
to top number
X’s go
in the
first
column
Factors come
from the
diagonals
3
5
15
15
1
1
1
3
5
n
n
First term
goes here
Third term
goes here
Multiply
across to get
this number
What factors
of 15 will add
to get 16?
Factors must multiply
across to last number
Factors multiply up
to top number
n’s go
in the
first
column
Factors come
from the
diagonals
3
-10
-30
What factors of
30 will subtract
to get 7?
10
3
-
Negatives transfer
to middle column
Does 3 go
into 10
evenly?
No, so put a
1 in this
place.
3
1
1
10
x
x
-
Which factor
needs to be
negative to
get a positive
7?
4
-15
-60
What factors of
60 will subtract
to get 4?
Factors of 60
1 * 60
2 * 30
3 * 20
4 * 15
5 * 12
6 * 10
6
-10
Negatives transfer
to middle column
-
Start with
the 4. It
can’t go
into either
6 or 10
evenly, so
we have to
split it to 2
and 2.
2
2
3
5
x
x
9
8
72
What factors of
72 will add to
get 17?
Factors of 72
1 * 72
2 * 36
3 * 24
4 * 18
6 * 12
8 * 9
-8
-9
-
-
8
9
1
1
x
x
If the trinomial
has a GCF, it
needs to be
removed first!
2
4
8
What factors of
8 will add to
get 9?
-8
-1
-
-
1
1
2
4
x
x
D
o
N
O
T
f
o
r
g
e
t
t
h
e
2
y
o
u
p
u
l
l
e
d
o
u
t
a
t
t
h
e
b
e
g
i
n
n
i
n
g
!
2
5
10
-10
-1
-
1
1
2
5
x
x
y
y
Y’s go in the
second column
-
3
-8
-24
Factors of 24
1 * 24
2 * 12
3 * 8
4 * 6
-4
6
-
3
1
4
2
x
x
y
y
C
ONTACT
I
NFORMATION
Jennifer Morgan
jennmorgan05@gmail.com
Christina Guynes
chguynes@kisd.esc18.net
Explore the techniques of factorization through Tic-Tac-Toe method and factor tables. Learn how to find pairs of numbers that multiply to a given result, factor polynomials correctly, and understand the importance of factoring in mathematics concepts. Engage with visual representations and step-by-step explanations to enhance your factorization skills.
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Presentation Transcript
TIC-TAC-TOE FACTORING Presented by: Jennifer Morgan and Christina Guynes Grady ISD Kermit ISD
DAY ONE FACTOR TABLES Find the pair of numbers that will multiply to make the bottom number and add to give you the top number. 7 9 10 3 4 6 4 5 4 12 20 24
FACTOR TABLES -5 -25 40 -3 -8 -21 4 4 36 3 -4 -7 -24 84 144 -28
TIC-TAC-TOE METHOD 7 2 + + x x 2 3 2 3 6 1 1 2 3 Factors must multiply across to last number Multiply across to get this number Third term goes here What factors of 6 will add to get 7? First term goes here 1 Factors multiply up x to top number X s go in the first column Factors come from the diagonals 6 2 ( x + + 1 )( ) 3 x x
+ + 2 3 16 5 n n Multiply across to get this number Third term goes here 3 5 15 1 1 3 5 n First term goes here What factors of 15 will add to get 16? 1 Factors multiply up n to top number n s go in the first column 15 Factors come from the diagonals Factors must multiply across to last number + ) 5 + 3 ( 1 )( n n
+ x 2 3 7 10 x What factors of 30 will subtract to get 7? 3 -10 -30 1 1 x Does 3 go into 10 evenly? Which factor needs to be negative to get a positive 7? 10 10 3 - x No, so put a 1 in this place. 3 - x Negatives transfer to middle column + 3 ( 10 )( ) 1 x
x 2 4 4 15 x What factors of 60 will subtract to get 4? Start with the 4. It can t go into either 6 or 10 evenly, so we have to split it to 2 and 2. 4 -15 -60 2 2 5 Factors of 60 1 * 60 2 * 30 3 * 20 4 * 15 5 * 12 6 * 10 3 6 -10 x - x Negatives transfer to middle column + 2 ( 5 )( 2 ) 3 x x
+ 2 9 17 8 x x What factors of 72 will add to get 17? 9 8 72 -8 9 1 Factors of 72 1 * 72 2 * 36 3 * 24 4 * 18 6 * 12 8 * 9 1 -8 -9 x - x ) 1 9 ( 8 )( x x
If the trinomial has a GCF, it needs to be removed first! + = + 2 2 4 18 8 2 ( 2 9 ) 4 x x x x What factors of 8 will add to get 9? 2 4 8 -1 1 2 4 ) 4 -1 x - -8 x Do NOT forget the 2 you pulled out at the beginning! 2 ( 2 1 )( x x
+ 2 2 2 11 5 x xy y 2 5 10 1 1 2 5 ) 5 y - -1 x y - -10 x y 2 ( )( x y x Y s go in the second column
+ 2 2 3 2 8 x xy y 3 -8 -24 - 3 2 Factors of 24 1 * 24 2 * 12 3 * 8 4 * 6 1 4 x -4 6 x y y + 3 ( 4 )( 2 ) x y x y
CONTACT INFORMATION Jennifer Morgan jennmorgan05@gmail.com Christina Guynes chguynes@kisd.esc18.net
