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) 35p^{3} - 25p^{2} - 56p + 40
b) 7r^{3} - 14r^{2} + 8r - 16
#2:
Instructions: Factor each using grouping.
a) 160mn + 15 - 40m - 60n
#3:
Instructions: Factor each using grouping.
a) 14xy - 12 - 42x + 4y
#4:
Instructions: Factor each using grouping.
a) 30bz - 16xc - 12bc + 40xz
#5:
Instructions: Factor each using grouping.
a) 5ah + 60bk + 15ak + 20bh
Written Solutions:
Solution:
a) (5p^{2} - 8)(7p - 5)
b) (7r^{2} + 8)(r - 2)
Solution:
a) 5(8m - 3)(4n - 1)
Solution:
a) 2(7x + 2)(y - 3)
Solution:
a) 2(3b + 4x)(5z - 2c)
Solution:
a) 5(a + 4b)(h + 3k)