Why does synthetic division use the opposite of the constant term in the divisor as the multiplying factor? Using the opposite of the constant term in the divisor as the multiplying factor in synthetic division causes all answers to be positive.

The process in polynomial long division is to divide, multiply, subtract, and bring down. Using the opposite of the constant term in the divisor for synthetic division allows for addition in the columns instead of subtraction.

Synthetic division is used to obtain an answer to the division of a polynomial by a constant.

Since the synthetic division assumes that the divisor has a leading coefficient of 1, the only thing that changes the sums is the constant in the divisor.