Factoring Flow Chart
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1FACTORING FLOW CHART
Factor out the GCF! (Reverse Distributive Property)
Then ask: How many terms are contained in the expression remaining to be factored?
Example
2
3
(
)
+
− =
+
−
2
2
1.
27
x y
9
xy
3
xy
3
xy
9
x
3
y
1
Is the expression a difference of squares,
Is the trinomial a Perfect
difference of cubes, or sum of cubes?
Square Trinomial (PST)?
Yes!
Yes!
No!
No!
4
Factor as follows:
Don't be fooled by the
Factor as follows:
Factor into 2 binomials.
(
)(
)
(
)
−
=
+
−
+
+
+
=
+
2
2
2
2
2
2
2
a
b
a b a b
sum of squares
a
b
!
a
2
ab b
a b
Some call this “unfoiling” or
(
)
(
)
(
)
−
=
−
+
+
−
+
=
−
2
3
3
2
2
2
2
It's PRIME!
“the puzzle” or guess & check
a
b
a b a
ab b
a
2
ab b
a b
(
)
(
)
+
=
+
−
+
3
3
2
2
a
b
a b a
ab b
Examples
Factor by Grouping.
Group the first two terms and the second two terms together.
Examples
Look for the common binomial factor.
Examples
Answer is the product of two binomials.
Example
(
)(
)
+
+
=
+
+
2
x
11
x
28
x
4
x
7
8.
(
)(
)
+
−
−
− − =
+
−
2
5. 24
ac
18
bc
28
ad
21
bd
6
x
x
15
2
x
3 3
x
5
9.
(
)(
)
(
) (
)
−
=
+
−
+
+ −
−
2
2
2.
9
x
4
y
3
x
2
y
3
x
2
y
24
ac
18
bc
28
ad
21
bd
group
(
)
(
)
(
)
(
)
−
=
−
+
+
+
−
+
3
2
3.
x
64
x
4
x
4
x
16
6 4
c a
3
b
7
d
4
a
3
b
gcf out of each
(
)
(
)(
)
(
)
(
)
+
−
+
=
+
−
+
+
+
=
+
2
3
2
2
4
a
3
b
6
c
7
d
4.
8
a
27
2
a
3
b
4
a
6
ab
9
answer
6.
x
8
x
16
x
4
(
)
−
+
=
−
2
2
7.
4
x
36
x
81
2
x
9
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