### About Factoring by Grouping:

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

#1:

Instructions: Factor each using grouping.

a) n^{3} - 4n^{2} + 3n - 12

b) 5b^{3} + 4b^{2} + 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 - 27x^{2}d + 45bd - 45x^{2}c

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#4:

Instructions: Factor each using grouping.

a) 24n^{2}mc - 75n^{3}k + 60n^{2}mk - 30n^{3}c

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#5:

Instructions: Factor each using grouping.

a) 72xy + 64n^{4} + 96xn^{3} + 48ny

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Written Solutions:

#1:

Solutions:

a) (n^{2} + 3)(n - 4)

b) (b^{2} + 4)(5b + 4)

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#2:

Solutions:

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

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

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#3:

Solutions:

a) 3(5b - 3x^{2})(5c + 3d)

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#4:

Solutions:

a) 3n^{2}(4m - 5n)(2c + 5k)

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#5:

Solutions:

a) 8(3x + 2n)(4n^{3} + 3y)