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
Factoring by Grouping Test:
#1:
Instructions: Factor each using grouping.
a) n^{3} - 4n^{2} + 3n - 12
b) 5b^{3} + 4b^{2} + 20b + 16
#2:
Instructions: Factor each using grouping.
a) 120xy - 160x - 48y + 64
b) 4mn - 12m - 10n + 30
#3:
Instructions: Factor each using grouping.
a) 75bc - 27x^{2}d + 45bd - 45x^{2}c
#4:
Instructions: Factor each using grouping.
a) 24n^{2}mc - 75n^{3}k + 60n^{2}mk - 30n^{3}c
#5:
Instructions: Factor each using grouping.
a) 72xy + 64n^{4} + 96xn^{3} + 48ny
Written Solutions:
Solution:
a) (n^{2} + 3)(n - 4)
b) (b^{2} + 4)(5b + 4)
Solution:
a) 8(5x - 2)(3y - 4)
b) 2(2m - 5)(n - 3)
Solution:
a) 3(5b - 3x^{2})(5c + 3d)
Solution:
a) 3n^{2}(4m - 5n)(2c + 5k)
Solution:
a) 8(3x + 2n)(4n^{3} + 3y)