Answer :
To solve the problem, we need to evaluate the expression inside the square root: [tex]\(\sqrt{12 - 33}\)[/tex].
1. Start by evaluating the expression inside the square root:
[tex]\[
12 - 33 = -21
\][/tex]
2. Since you cannot take the square root of a negative number in the set of real numbers, the expression [tex]\(\sqrt{-21}\)[/tex] is not defined in the context of real numbers.
3. Therefore, in this scenario, synthetic division or any operation involving a remainder does not apply because the given expression does not result in a real number that allows for division or calculation of a remainder.
Because [tex]\(\sqrt{12 - 33}\)[/tex] does not result in a real number used in synthetic division, it means there is no valid remainder that can be calculated for this problem in the traditional sense given the choices provided.
Therefore, none of the options (A, B, C, D) are applicable because the scenario described cannot occur under the rules of synthetic division in real number arithmetic.
1. Start by evaluating the expression inside the square root:
[tex]\[
12 - 33 = -21
\][/tex]
2. Since you cannot take the square root of a negative number in the set of real numbers, the expression [tex]\(\sqrt{-21}\)[/tex] is not defined in the context of real numbers.
3. Therefore, in this scenario, synthetic division or any operation involving a remainder does not apply because the given expression does not result in a real number that allows for division or calculation of a remainder.
Because [tex]\(\sqrt{12 - 33}\)[/tex] does not result in a real number used in synthetic division, it means there is no valid remainder that can be calculated for this problem in the traditional sense given the choices provided.
Therefore, none of the options (A, B, C, D) are applicable because the scenario described cannot occur under the rules of synthetic division in real number arithmetic.
