College Algebra & Trigonometry, 2018a

1.2. FACTORING 21
1 24
2 12
3 8
4 6
We can see that the factor pair of 24 that adds up to 10 is 6 ∗ 4. We proceed by
splitting the 10x into 6x +4x and then factor by grouping. If you are uncomfortable
with factoring by grouping, then this is probably not a good method to
try. However, if you are comfortable with factoring by grouping, the rest of the
process is relatively straightforward:
3x 2 +10x +8=3x 2 +6x +4x +8
We then factor a common factor from the first two terms and the last two terms
separately, and then factor out the common binomial factor of (x +2):
3x 2 +10x +8=3x 2 +6x +4x +8
=3x(x +2)+4(x +2)
=(x + 2)(3x +4)
Example
Factor 7x 2 − 5x − 18
In this example, the sign of the constant term is negative, which means that we’ll
need factor pairs that produce a difference of 5. The leading coefficient is 7, which
is prime, so, again, the only way to split up the 7 is 7 ∗ 1.
(7x ?)(x ?)
The options for filling in the question marks come from the factors of 18, for