Answer: First off thats not how you ask for help, by calling us "smart math people" that could offend someone...Second off the answer is 10 because
Step-by-step explanation:
A^2 + B^2 = C^2
6^2 + 8^2 = C^2
36 + 64 = 100 square root that = 10
Answer: 10
By either long or synthetic division, it's easy to show that

The quartic will be exactly divisible by

when the numerator of the remainder term vanishes, or for those values of

such that

I'm not sure how to count the number of solutions (software tells me it should be 80), but hopefully this is a helpful push in the right direction.
The answer for this is 224