9, 24, and 7 have no common factor except for 1. However, to factor the above expression, we need to list down the factors of the first term and the last term first.
The factors of the first term 9 are 3 and 3, and 1 and 9.
The factors of the last term 7 are just 1 and 7, and -1 and -7.
The next thing to do is to pair the factors of the first term to the factors of the last term and multiply them to each other then, add. If we get the value of the middle term 24, then, we've got the right pair!
Let's see.
3 and 3, and 1 and 7 = 3(1) + 3(7) = 3 + 21 = 24. Wow! We got it the first time. Therefore, the factor of the above expression is (3m + 1)(3m + 7).
