When we factor a trinomial with a leading coefficient that is ≠ 1, we generally use two different techniques. We can use reverse FOIL. This method involves trial and error to find the right combination. Secondly, we can rewrite our trinomial as a four term polynomial and use factoring by grouping.
Test Objectives:•Demonstrate a general understanding of factoring a trinomial
•Demonstrate the ability to factor a trinomial using reverse FOIL
•Demonstrate the ability to factor a trinomial using factoring by grouping
Factoring Trinomials with a Leading Coefficient that is ≠ 1 Test:
#1:
Instructions: Factor each.
a) 3a^{2} - 20a - 100
#2:
Instructions: Factor each.
a) 15n^{2} - 95n + 100
#3:
Instructions: Factor each.
a) 18b^{2} + 15b - 12
#4:
Instructions: Factor each.
a) 8k^{2} - 42k + 10
#5:
Instructions: Factor each.
a) 54x^{2} - 336xy + 72y^{2}
Written Solutions:
Solution:
a) (3a + 10)(a - 10)
Solution:
a) 5(3n - 4)(n - 5)
Solution:
a) 3(2b - 1)(3b + 4)
Solution:
a) 2(4k - 1)(k - 5)
Solution:
a) 6(9x - 2y)(x - 6y)