High School

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------------------------------------------------ What is the remainder in the synthetic division problem below?

[tex]\sqrt{12-32}[/tex]

A. 5
B. 4
C. 3
D. 2

Answer :

To solve the problem, we need to understand a couple of things. First, let's look at the expression inside the square root: [tex]\( \sqrt{12 - 32} \)[/tex].

1. Calculate the expression inside the square root:

- We have [tex]\( 12 - 32 \)[/tex].
- Subtracting these numbers gives us [tex]\(-20\)[/tex].

2. Analyze the square root of a negative number:

- In the real number system, the square root of a negative number is not defined. So, [tex]\( \sqrt{-20} \)[/tex] does not have a real number solution.

This tells us that there may be a misunderstanding in how the question is presented because the square root of a negative number is not something we can work with in synthetic division.

Therefore, if we are looking at the expression [tex]\( \sqrt{12 - 32} \)[/tex] and calculating it straightforwardly without considering any further context about synthetic division, the number inside the square root is [tex]\(-20\)[/tex], which means the square root itself is not applicable in the real number system.

In conclusion, the calculation itself yields [tex]\(-20\)[/tex], indicating a possible error in the context of the question referring to synthetic division specifically. Thus, among the choices for the remainder of a synthetic division problem, the question doesn't fit traditional expectations based directly on the presented content.