### 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

#1:

Instructions: Factor each using grouping.

a) 35p^{3} - 25p^{2} - 56p + 40

b) 7r^{3} - 14r^{2} + 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:

Solutions:

a) (5p^{2} - 8)(7p - 5)

b) (7r^{2} + 8)(r - 2)

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#2:

Solutions:

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

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#3:

Solutions:

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

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#4:

Solutions:

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

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#5:

Solutions:

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