Factoring by
Grouping
Notes 8-2B
I. Factoring By Grouping
Ex 1. Factor 4ab + 8b + 3a + 6
This polynomial cannot be factored by pulling out a GCF
To factor this polynomial we will use a method called Factoring
By Grouping to break down the problem and make it more
simple to factor.
4ab + 8b + 3a + 6
(4ab + 8b) (3a + 6)
4b(a + 2)
3(a + 2)
(a + 2)(4b + 3)
Three easy steps:
1. Group terms with common
factors
2. Factor the GCF from each
grouping
3. Factor out the common term
using the Distributive Property
CHECK! Using FOIL or Distribution
Factoring By Grouping
Ex 2. Factor each polynomial.
6x2 – 15x – 8x + 20
(6x2 – 15x) (-8x + 20)
3x(2x – 5)
– 4(2x – 5)
(2x – 5)(3x – 4)
1. Group terms with common
factors
2. Factor the GCF from each
grouping
3. Factor out the common term
using the Distributive Property
CHECK! Using FOIL
Factoring By Grouping
Ex. Factor each polynomial.
12y2 - 9y - 8y + 6
(12y2 - 9y)
3y(4y - 3)
(-8y +6)
-2(4y - 3)
(4y - 3)(3y - 2)
1. Group terms with common
factors
2. Factor the GCF from each
grouping
3. Factor out the common term
using the Distributive Property
CHECK! Using FOIL or Distribution
Factoring By Grouping
1. x2 + 2x + 3x + 6
(x2 + 2x) (3x + 6)
x(x + 2)
PRACTICE
3(x + 2)
(x + 2)(x + 3)
2. 2my + 7x + 7m + 2xy
(2my + 2xy)
(7x + 7m)
2y(m + x)
7(x + m)
(m + x)(2y + 7)
Note: it is sometimes
necessary to use
the commutative
property to regroup
the terms…