College Algebra & Trigonometry, 2018a

18 CHAPTER 1. ALGEBRA REVIEW
Here, we can see that the factors 3 and 14 have a difference of 11. This means that
we will use these factors in our answer: (x 3)(x 14). In determining how
to place the + and − signs in the parentheses, we can refer back to the original
problem: x 2 +11x − 42. If we want a difference of (+11x), then we’ll need to have
a (+14) and a (−3):
Example
Factor x 2 +28x +96
x 2 +11x − 42 = (x − 3)(x + 14)
In this problem, the sign of the constant term is positive. That means that we
need factors of 96 that add up to 28. A systematic exploration of all the factor
pairs of 96 can help us to find the correct pair:
1 96
2 48
3 32
4 24
6 16
8 12
Here, we can see that the factors 4 and 24 add up to 28. This means that we will
use these factors in our answer: (x 4)(x 24). In determining how to place
the + and − signs in the parentheses, we can refer back to the original problem:
x 2 +28x +96. If we want 4 and 24 to add up to (+28), then they should both be
positive:
x 2 +28x +96=(x +4)(x + 24)