Final answer:
The student cannot use synthetic division to divide the given polynomial by (x+7) because it is not of the form (x-a) where 'a' is a constant.
Step-by-step explanation:
The student cannot use synthetic division to divide the polynomial m³+m²-36m+42 by (x+7) because synthetic division is only applicable when dividing by a linear binomial of the form (x-a). In this case, (x+7) is a linear binomial since it is of the form (x-a), but it is not of the form (x-a) where 'a' is a constant. Synthetic division can only be used when dividing by a linear binomial where 'a' is a constant.