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