Answer :

Final answer:

The question pertains to synthetic division, used to divide polynomials by a binomial, where the divisor is represented by the zero of the linear factor. Although the specific format from the student was unclear, the divisor in this context is likely the binomial (x - 2), derived from the leftmost number '2' in the bottom row.

Explanation:

The student's question involves synthetic division, which is a shorthand method of polynomial division, particularly when dividing by a linear factor, and only requires the use of the coefficients. The divisor in a synthetic division setup corresponds to the zero of the linear factor involved in the division. If the synthetic division setup provided by the student is '2 10 1 5 -5 -10 0 -5', this likely represents the coefficients of a polynomial being divided by a binomial. Since synthetic division is generally used to divide by a binomial of the form x - k, where k is the root of the polynomial, the top row should represent the coefficients in descending order of the polynomial, and the leftmost number in the bottom row (in this case, the '2') represents the root of the divisor.

To determine the exact divisor, we would need the specific format and arrangement of the synthetic division presented by the student to be corrected. Nonetheless, the divisor would likely be in the form of (x - 2) because in synthetic division you use the root of the binomial divisor, which in this case is '2'.

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