1. The HCF is 4x^2, not 4x^3...
2. Correct
3. You are expected to know that if you can find a z = a such that f(a) = 0, then (z - a) is a factor. You are also expected to know that a can only be factors of 48...
Once you have found a factor (z - a), long divide, follow the same process again with the remaining factor until it's completely factorised.