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Answer :
Sure! Let's perform the synthetic division step-by-step to find the remainder when 1 is divided by 4.
### Step-by-Step Solution:
1. Set Up the Problem:
We are to divide 1 by 4. In the context of synthetic division, you consider the divisor (4) and the dividend (1).
2. Perform the Division:
In synthetic division, you're looking to see how many times the divisor (4) can fit into the dividend (1). Since 4 cannot fit into 1 any whole number of times, there’s no complete division that can occur for the number 4.
3. Identify the Remainder:
Since 4 cannot be divided into 1, the remainder is simply 1. In other words, 1 divided by 4 leaves 1 as the remainder because 4 cannot go into 1 at all.
Therefore, the remainder for this synthetic division problem is 1.
Given the options:
- A. 7
- B. 3
- C. 5
- D. 9
None of these match, because the actual remainder is 1. It seems there was a mistake in providing or aligning the options with the possible remainders. The correct remainder based on our steps should be 1.
### Step-by-Step Solution:
1. Set Up the Problem:
We are to divide 1 by 4. In the context of synthetic division, you consider the divisor (4) and the dividend (1).
2. Perform the Division:
In synthetic division, you're looking to see how many times the divisor (4) can fit into the dividend (1). Since 4 cannot fit into 1 any whole number of times, there’s no complete division that can occur for the number 4.
3. Identify the Remainder:
Since 4 cannot be divided into 1, the remainder is simply 1. In other words, 1 divided by 4 leaves 1 as the remainder because 4 cannot go into 1 at all.
Therefore, the remainder for this synthetic division problem is 1.
Given the options:
- A. 7
- B. 3
- C. 5
- D. 9
None of these match, because the actual remainder is 1. It seems there was a mistake in providing or aligning the options with the possible remainders. The correct remainder based on our steps should be 1.
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