We describe a high-school student’s difficulties in understanding the notation for a
general polynomial: ... 1 1 2 + + + + − − x x x n n during a CAS-based activity to develop a
general factorization for −1 n x . We illustrate how he attributes a meaning to the
ellipsis symbol related to his experience of “terms cancelling out” rather than the
taken-for-granted meaning of an undefined continuing process. We show his
associated difficulties in making sense of the sequence of decreasing exponents.
Finally, emerging from his misunderstandings, we describe his motivation to find a
general formula for x n +1, testing his conjectures using the CAS