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Rainbow Factoring Lesson
    To factor by grouping,
place the 4 terms in the box:
2c2+8c+3c+12
2c2
3c
?
8c
12
?
Type the GCF of each row and column
Factor:
2c2
3c
2c2+8c+3c+12
c
8c
12
2c
3
Factor:
2c2
3c
c
8c
12
2c2+8c+3c+12
4
(2c2+8c)(3c+12)
(2c+3)(c+4)
2c2+8c+3c+12
Factored  is:
There are many
ways to split +11c.

Use the chart to show
a few terms that
simplify to +11c:
This trinomial can
be factored by
grouping IF
you split +11c
into two terms.
Factor:
2c2+8c+3c+12
+8c
+6c
+7c
2c2+11c+12
+3c
?
+4c
?
+5c
?
=
=
=
11c
11c
11c
Why was
+8c+3c
selected?
Click
OK
Factor:
2c2+8c+3c+12
+8c
+6c
+7c
2c2+11c+12
+3c
+4c
+5c
=
=
=
11c
11c
11c
11c was
split into
+8c and +3c
because
the only way
you can
factor by
grouping...
2c2+8c+3c+12
2c2+11c+12
 Is to have the
 product of the

outside     terms
equal the product
        of the
inside terms
The only way you can factor by grouping

is if the product of the

equals the product of the
Which polynomial will factor by grouping?
9x+4x
 6x+5x
3x2 +6x+5x +10
3x2 +9x+4x +10
outside  terms
inside terms
The only way you can factor by grouping

is if the product of the

equals the product of the
Which polynomial will factor by grouping?
9x+4x
 6x+5x
4x2 +8x+5x +10
4x2 +7x+7x +10
outside  terms
inside terms
Which polynomial will factor by grouping?
9x+4x
 6x+5x
outside
3x2 +3x+8x +10
3x2 +9x+4x +12
inside terms
Product
terms
Which polynomial will factor by grouping?
9x+4x
 6x+5x
outside
2x2 +6x+3x +9
2x2 +9x+4x +9
inside terms
Product
terms
"Rainbow"
Factoring
multiplies
the 2
outside
terms to
split
the
middle
term.
2c2 +7c +6
What factor pair of
Click
OK
   Has
a sum of
12
Factor Pairs
1
12
*
*
*
4
2c2 +7c +6
What factor pair of
   Has
a sum of
12
Which factor pair
of 12 has a sum of
7?
Factor Pairs
2
1
3
12
*
*
*
12
4
6
2c2 +7c +6
What factor pair of
1 and 12
2 and 16
3 and 4
   Has
a sum of
12
You  have 4 terms,
now factor by grouping
3 and 4
   Which
factor pair
   of 12
has a sum
   of 7?
2c2+3c+4c+6
2c2 +7c +6
What factor pair of
   Has
a sum of
12
Click OK
c
Fill in GCFs
of each row
& column
2c2
4c
3c
6
2c2+3c+4c+6
2c2 +7c +6
What factor pair of
   Has
a sum of
12
Type the
missing factor
(no spaces)
c
2
2c2
4c
2c
3c
6
3
2c2+3c+4c+6
(c+2)
2c2 +7c +6
What factor pair of
   Has
a sum of
12
(       )
c
2
Click OK
2c2
4c
2c
3c
6
3
2c2+3c+4c+6
(c+2)
2c2 +7c +6
What factor pair of
   Has
a sum of
(2c+3)
12
1. Multiply the outside terms to get
the master product on TOP of the rainbow
5c2 +13c +6
What factor pair of
   Has
a sum of
Use 30,
the master
product,
to split the
middle term.
What factor pair of 30 has a sum of +13?
5 and 6
5 and 8
3 and 10
2 and 15
5c2 +13c +6
What factor pair of
   Has
a sum of
30
Use the box
to factor by
grouping
10c
5c2
3c
6
5c2+3c+10c+6
5c2 +13c +6
What factor pair of
   Has
a sum of
30
Use GCFs to
write the
polynomial
in factored
form
2
c
10c
5c2
5c
3c
6
3
5c2+3c+10c+6
5c2 +13c +6
Factored form:
(5c2+3c)(10c+6)
(5c+3)(c+2)
What factor pair of
   Has
a sum of
30
1. Multiply the outside terms to get
the master product on TOP of the rainbow
5c2 +13c -6
What factor pair of
    Has
a diff. of
Use ,
the master
product,
to split the
middle term.
What factor pair
of -30 has
a difference
of +13?
-30
5c2 +13c -6
What factor pair of
    Has
a diff. of
3 and 10
-3 and 10
2 and -15
-2 and 15
-30
Use the box
to factor by
grouping
15c
5c2
-2c
-6
5c2-2c+15c-6
5c2 +13c -6
What factor pair of
    Has
a diff. of
-30
c
3
Use GCFs to
write the
polynomial
in factored
form
15c
5c2
5c
-2c
-2
-6
5c2-2c+15c-6
5c2 +13c -6
(5c2-2c)(15c-6)
(c+3)(5c-2)
Factored form:
What factor pair of
    Has
a diff. of
-30
N
D
H
T
E
E
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