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) 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:
Solutions:
a) (n2 + 3)(n - 4)
b) (b2 + 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 - 3x2)(5c + 3d)
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#4:
Solutions:
a) 3n2(4m - 5n)(2c + 5k)
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#5:
Solutions:
a) 8(3x + 2n)(4n3 + 3y)
