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Factoring by Grouping Test
About Factoring by Grouping:

When we encounter a four term polynomial, in some cases we can factor out a common binomial factor using a process known as factoring by grouping. To factor using grouping, we arrange our polynomial into two groups of two. We then pull out the GCF or -(GCF) from each group. We look to see if we have a common binomial factor. If we do not, we can sometimes find one by using a different grouping.

Test Objectives:

•Demonstrate the ability to find the GCF for a group of terms

•Demonstrate the ability to factor out the GCF or -(GCF) from a group of terms

•Demonstrate the ability to factor a four term polynomial using grouping

Factoring by Grouping Test:




#1:


Instructions: Factor each using grouping.


a) 35p3 - 25p2 - 56p + 40


b) 7r3 - 14r2 + 8r - 16


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#2:


Instructions: Factor each using grouping.


a) 160mn + 15 - 40m - 60n


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#3:


Instructions: Factor each using grouping.


a) 14xy - 12 - 42x + 4y


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#4:


Instructions: Factor each using grouping.


a) 30bz - 16xc - 12bc + 40xz


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#5:


Instructions: Factor each using grouping.


a) 5ah + 60bk + 15ak + 20bh


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Written Solutions:




#1:


Solution:


a) (5p2 - 8)(7p - 5)


b) (7r2 + 8)(r - 2)


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#2:


Solution:


a) 5(8m - 3)(4n - 1)


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#3:


Solution:


a) 2(7x + 2)(y - 3)


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#4:


Solution:


a) 2(3b + 4x)(5z - 2c)


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#5:


Solution:


a) 5(a + 4b)(h + 3k)


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