Final answer:
The question seems to confuse synthetic division with the division of exponentials. For division of exponentials, we divide the coefficients and subtract the exponents. Additional information is required to ascertain the remainder from a synthetic division operation.
Step-by-step explanation:
When considering synthetic division and specifically looking at the remainder post-division, we must carefully evaluate the coefficients involved and the degree of the dividend and the divisor. Synthetic division is used primarily for dividing polynomials, and the remainder is the last term obtained in the process. However, the text provided seems to be centered more on the division of exponentials which is a slightly different concept.
In cases of division of exponentials, subtracting the exponents is key. When presented with terms that are exponentials, we divide the numerical coefficients and subtract the exponents where the base is the same. For example, given 2.56 × 10^-38 ÷ 5 × 10^-21, we first divide 2.56 by 5, and then subtract the exponent of the divisor (-21) from that of the dividend (-38) to get a new exponent. In this case, it would be 1,024 × 10^-18 after performing the necessary calculations and simplifications.
Without the specific polynomial coefficients and degrees, we cannot determine the exact remainder. Additional information would be needed to complete a synthetic division problem.