If (t-8) is a factor of t^2-kt-48, then k=

-6
-2
2
6
14

The OA is C. However I got B. Although I understand the Official Guide's way of solving it, I solved it in the following manner and got a different answer:
t^2-kt-48 then it follows that
(t-8)(t+6) =0 (Because -8*6=-48) Therefore;
k must be the sum of -8 and 6, which is -2 option B. Can anyone tell me where I went wrong? Thanks

The Official Guide solves it by plugging 8 in for t and solving the equation. Again, I understand why/how this works, but I don't understand why/how my approach is wrong.

Thanks