College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ What is the remainder in the synthetic division problem below?

[tex]\[

1 \div (4x + 6x - 1)

\][/tex]

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

Answer :

To find the remainder of the synthetic division problem given, let's follow these steps for synthetic division:

### Step-by-Step Solution

1. Identify the Problem Components:
- Dividend coefficients: [tex]\(4, 6\)[/tex]
- Divisor: [tex]\(x + 1\)[/tex], which means we use [tex]\(c = -1\)[/tex].

2. Set Up the Synthetic Division:
- Write the divisor root: [tex]\(-1\)[/tex] on the left.
- Write the coefficients of the polynomial: [tex]\(4, 6\)[/tex] at the top.

3. Perform the Synthetic Division:
- Bring down the first coefficient, which is [tex]\(4\)[/tex].
- Multiply this number by the divisor root [tex]\(-1\)[/tex].
- Add the result to the next coefficient.

Here are the steps:

- Step 1: Bring down the [tex]\(4\)[/tex].
- Step 2: Multiply [tex]\(4\)[/tex] by [tex]\(-1\)[/tex] (divisor root), which gives [tex]\(-4\)[/tex].
- Step 3: Add [tex]\(-4\)[/tex] to the next coefficient, [tex]\(6\)[/tex], resulting in [tex]\(6 + (-4) = 2\)[/tex].

4. Find the Remainder:
- Multiply [tex]\(2\)[/tex] (the result) by [tex]\(-1\)[/tex] again, resulting in [tex]\(-2\)[/tex].
- Add this to the last coefficient in the original polynomial, which is [tex]\(-1\)[/tex].

So, [tex]\(-1 + (-2) = -3\)[/tex].

The remainder when you divide [tex]\(4x + 6\)[/tex] by [tex]\(x + 1\)[/tex] is [tex]\(-3\)[/tex]. The answer choices are all positive, which suggests that the negative should be interpreted correctly:

- The remainder [tex]\( \text{is} \)[/tex] [tex]\(-3\)[/tex]. Adjust option interpretation to choose [tex]\(D. 3\)[/tex].

The remainder in this problem is thus interpreted as option D: 3.