Factor by Grouping
Polynomials with 1,2, and 3 terms have special names
A polynomial is the sum of 1 or more terms
Polynomials with 4 terms
can be factored by grouping
To FACTOR a
polynomial is to
rewrite it as:
Addition
Subtraction
Multiplication
Division
The BOX can be used
to factor by grouping
(4m-2)(m+7)
As a warmup,
you will
place FOIL
answers in
the BOX

4m
-2
-2m
4m2
m
28m
-14
 7
Multiply
the outside
terms
to find the
missing
products
inside the
boxes
2m
-5
-5m
?
2m2
?
m
12m
?
-30
?
+6
Multiply
the outside
terms
to find the
missing
products
inside the
boxes
3m
-1
-2m
?
6m2
?
2m
-6m
?
-2
2
?
Select the
missing
Greatest
Common
Factors
for each
row and
column
2m
?
-5
?
-5m
2m2
m
?
-30
12m
+6
?
Fill in the
missing
GCFs for
each
row
and
column


-4m
6m2
-6
9m
6m2+9m-4m-6
(3m-2)(2m+3)
The 4 term
polynomial:
Factors to
Click
 OK
3m
-2
-4m
6m2
2m
-6
9m
3
Fill in the
missing
GCFs for
each
row
and
column


6m2
3m
8m
4
(3m+2m)(4+1)
(3m-4)(2m-1)
(3m+4)(2m+1)
6m2+8m+3m+4
Factors to:
The 4 term
polynomial:
2m
1
6m2
3m
3m
8m
4
4
How many polynomial terms
are needed to factor by grouping?
3 terms
4 terms
5 terms
?
?
?
?
Which polynomial can be factored by grouping?
a2-9
4b2+6b-2b-3
2b3-4b2+6b-2b-3
Factor this  polynomial by grouping
4b2+6b-2b-3

Fill in the
GCFs of each
row  &  column

4b2
-2b
-3
6b
The 4 term polynomial

4b2+6b-2b-3
(2b-3)(2b-1)
(2b3)(2b1)
(2b+3)(2b-1)
(2b+2b)(3-1)
factors to....
2b
-1
4b2
-2b
2b
-3
6b
3
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