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Factoring by Grouping Test

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 Test:

#1:

Instructions: Factor each using grouping.

a) n3 - 4n2 + 3n - 12

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

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#2:

Instructions: Factor each using grouping.

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

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

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#3:

Instructions: Factor each using grouping.

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

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#4:

Instructions: Factor each using grouping.

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

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#5:

Instructions: Factor each using grouping.

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

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Written Solutions:

#1:

Solution:

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

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

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#2:

Solution:

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

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

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#3:

Solution:

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

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#4:

Solution:

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

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#5:

Solution:

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

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