Factoring by Grouping is a method used to factor a four-term polynomial. It involves separating a four-term polynomial into two groups and factoring the GCF from each group. Once this is done, the goal is to have a common binomial factor that can be factored out.

Test Objectives
• Demonstrate a general understanding of factoring by grouping
• Demonstrate the ability to factor out the greatest common factor (GCF) for a polynomial
• Demonstrate the ability to factor a four-term polynomial using grouping
Factoring by Grouping Practice Test:

#1:

Instructions: Factor each using grouping.

a) n3 - 4n2 + 3n - 12

b) 5b3 + 4b2 + 20b + 16

#2:

Instructions: Factor each using grouping.

a) 120xy - 160x - 48y + 64

b) 4mn - 12m - 10n + 30

#3:

Instructions: Factor each using grouping.

a) 75bc - 27x2d + 45bd - 45x2c

#4:

Instructions: Factor each using grouping.

a) 24n2mc - 75n3k + 60n2mk - 30n3c

#5:

Instructions: Factor each using grouping.

a) 72xy + 64n4 + 96xn3 + 48ny

Written Solutions:

#1:

Solutions:

a) (n2 + 3)(n - 4)

b) (b2 + 4)(5b + 4)

#2:

Solutions:

a) 8(5x - 2)(3y - 4)

b) 2(2m - 5)(n - 3)

#3:

Solutions:

a) 3(5b - 3x2)(5c + 3d)

#4:

Solutions:

a) 3n2(4m - 5n)(2c + 5k)

#5:

Solutions:

a) 8(3x + 2n)(4n3 + 3y)