College Algebra & Trigonometry, 2018a

1.2. FACTORING 23
If we want to try the other method for factoring 7x 2 − 5x − 18, we would multiply
7 ∗ 18 = 126, and then work to find factor pairs of 126 that have a difference of 5:
1 126
2 63
3 42
6 21
7 18
9 14
Here, the last factor pair, 9 ∗ 14, has a difference of 5. So then we proceed to factor
by grouping:
7x 2 − 5x − 18 = 7x 2 +9x − 14x − 18
= x(7x +9)− 2(7x +9)
=(7x +9)(x − 2)
Notice that when the −2 was factored out from the last two terms −14x − 18, we
ended up with −2(7x +9), because (−2) ∗ (+9) = −18. This is also important because
in order to factor out the common binomial factor of (7x +9), this binomial
must be exactly the same in both terms.