Since the product is negative, -264, the factors have opposite signs. Since the sum is odd, those factors cannot be both even or odd.
-264 = -8(33) which satisfies the sum of 25.
How to think in order to find factors of 264?
The greatest dividend closer to 26 is 24 which leaves a difference of 2. So we have: 24|24.
The greatest divisors are 12|12, which gives us 12*22, but they are both even.
So we try 8|8, which gives us 8*33 and it works.
-239
-1639
25
222
25
-79
228
4 x 25
4 and 25
-25
259
129