This is a trinomial of the form where a = 1, so we only have to consider the factors of c and the sum of those factors that equal b.
Step 1:
Look at the sign on the constant term. In this case it is negative. That means that the factors of -60 in this case must be of opposite signs. Now we know that the factors of the trinomial are going to look like this:
(x + __ )
(x - __ )
Step 2:
We need to find two integers, call them p and q such that pq = -60 and p + q = -11. Let's start with some possibilities:
p * q = -60
-3 * 20 = -60
3 * -20 = -60
-4 * 15 = -60
4 * -15 = -60
-5 * 12 = -60
5 * -12 = -60
-6 * 10 = -60
6 * -10 = -60
Now, for each of the choices of p and q above, which pair, when added together will yield -11? The only pair that has a difference of 11 is 4 and 15, but since the result must be -11, the negative sign needs to be on the 15, so now we have our p and q and we can simply plug those numbers into our factor pattern we established in Step 1.
