"Factoring Reference Sheet"

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A Factoring Flowchart
Factor Out
The GCF
Binomial
Trinomial
Larger
Perfect Square
Difference of
Grouping
Trinomial
Two Squares
.
Grouping is the only option
(
)
(
)
(
)
− b
= a + b
a − b
+ 2ab + b
= a + b
2
2
2
2
2
a
a
(
)
− 2ab + b
= a − b
2
2
2
a
Difference of
Two Cubes
a = 1
(
)
(
)
− b
= a − b
+ ab + b
3
3
2
2
a
a
What multiplies to
c
make
and adds to
b
make
?
Sum of
Two Cubes
(
)
(
)
+ b
= a + b
− ab + b
3
3
2
2
a
a
a ≠ 1
What multiplies to
ac
make
and adds
b
to make
?
OR
Trial and Error
REMEMBER
1. Always factor completely. After any step of factoring, look at each new factor to see
if you can factor it any further.
2. Check you answers. Multiplying your answers out using distribution.
A Factoring Flowchart
Factor Out
The GCF
Binomial
Trinomial
Larger
Perfect Square
Difference of
Grouping
Trinomial
Two Squares
.
Grouping is the only option
(
)
(
)
(
)
− b
= a + b
a − b
+ 2ab + b
= a + b
2
2
2
2
2
a
a
(
)
− 2ab + b
= a − b
2
2
2
a
Difference of
Two Cubes
a = 1
(
)
(
)
− b
= a − b
+ ab + b
3
3
2
2
a
a
What multiplies to
c
make
and adds to
b
make
?
Sum of
Two Cubes
(
)
(
)
+ b
= a + b
− ab + b
3
3
2
2
a
a
a ≠ 1
What multiplies to
ac
make
and adds
b
to make
?
OR
Trial and Error
REMEMBER
1. Always factor completely. After any step of factoring, look at each new factor to see
if you can factor it any further.
2. Check you answers. Multiplying your answers out using distribution.
Examples
(
)
x − 40b
x = 10x a
− 4b
2
2
2
2
1.
GCF
10a
(
)
(
)
= 10x a + 2b
a − 2b
Difference of 2 Squares
(
)
− 64a = 4a t
− 16
4
4
2.
GCF
4at
(
)
(
)
= 4a t
+ 4
− 4
2
2
t
Difference of 2 Squares
(
)
(
)
(
)
= 4a t
+ 4
t + 2
t − 2
2
Difference of 2 Squares
(
)
(
)
− a
− b
+ b
= a
− a
+ −b
+ b
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
a
x
y
x
y
x
y
x
y
3.
Grouping
(
)
(
)
= a
− y
− b
− y
2
2
2
2
2
2
x
x
Factoring Each Group
(
)
(
)
= a
− b
− y
2
2
2
2
x
GCF
(
)
(
)
(
)
(
)
= a + b
a − b
x + y
x − y
Difference of 2 Squares
(
)
− 205x − 30 = 5 30x
− 41x − 6
2
2
150x
4.
GCF
(
)
= 5 30x
− 45x + 4x − 6
2
ac=-180, b=-41
(
)
(
)
(
)
= 5 30x
− 45x
+ 4x − 6
2
Grouping Inside
(
)
(
)
(
)
= 5 15x 2x − 3
+ 2 2x − 3
Factoring Each Group
(
)
(
)
= 5 15x + 2
2x − 3
GCF
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