College

What is the remainder in the synthetic division problem below?

[tex]\[ 1 \longdiv { 4 } 6 \][/tex]

A. 7
B. 3
C. 5
D. 9

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.