Final answer:
The expression 4h² + g is already in its simplest form and cannot be factored further, hence it is considered a 'prime' expression.
Step-by-step explanation:
The student has been asked to factor the expression 4h² + g completely. Since there is no common factor between 4h² and g, and because they are not part of a larger recognizable pattern such as a difference of squares, sum of cubes, or other factorable forms, the expression is already in its simplest form. Therefore, the correct answer is 'c. Prime', which means that the expression cannot be factored further over the integers.