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) $$75bc - 27x^2d + 45bd - 45x^2c$$
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#4:
Instructions: Factor each using grouping.
a) $$24n^2mc - 75n^3k + 60n^2mk - 30n^3c$$
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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) $$8(3x + 2n)(4n^3 + 3y)$$
