Tom F. is absolutely right. Here's some explanation to go with it.
Factor: 12m^2 - 10m + 2
The first step when you factor should always be to look for a Greatest Common Factor, or GCF. If you can find one, you will usually make the problem quite a lot easier!
In this case, each of the terms is divisible by 2. So the first step is to factor out that 2.
2 ( 6m^2 - 5m + 1)
Now you look at the constant. It's 1. You can only get 1 as the constant if you multiply 1 * 1, or -1 * -1. So you look at the middle term. It's negative, so you must use -1 * -1. So, now set up what you know:
2 ( ?m - 1) (?m - 1)
To figure out the last part, the ?s, you have to find the factors of 6 that add up to 5. The factors of 6 are 6 and 1, or 2 and 3. So, 6+1 is 7, and 2+3 is 5. Ah, there's your 5! You know you need positive numbers, because you already have the two negative 1s. So you put in the 2 and 3:
2 (2m - 1) (3m - 1)
To check, you can multiply the whole thing out again and see if you get your original problem.
--Louise
