If 3a2 – 5ab – 2b2 is factored, one of the factors might be:

We want to factor 3a² - 5ab - 2b².

Note that 
(3a)*(-2b) + a*b = -6ab + ab = -5ab
(3a)*a = 3a²
b*(-2b) = -2b²

Therefore
3a² - 5ab - 2b² = (3a + b)(a - 2b)

The factors are (3a + b) and (a - 2b).

One of the factors is (3a + b).
Another factor is (a - 2b).