Answer :
Certainly! Let's go through the process of solving this synthetic division problem step by step.
We are given the coefficients of a polynomial: [tex]\(1, 4, 6\)[/tex]. These correspond to the polynomial [tex]\(f(x) = 1x^2 + 4x + 6\)[/tex].
The divisor root, based on the setup of the problem, is [tex]\(-1\)[/tex]. This means we are dividing the polynomial by [tex]\(x + 1\)[/tex].
Synthetic Division Steps:
1. Set up the synthetic division: Write the coefficients of the polynomial in a row: [tex]\(1, 4, 6\)[/tex].
2. Write the root of the divisor (opposite sign of the given value): Since [tex]\(x + 1\)[/tex] is the divisor, we use [tex]\(-1\)[/tex].
3. Bring down the leading coefficient: Start by bringing down the first coefficient [tex]\(1\)[/tex] as is. It represents the new leading coefficient after division.
4. Multiply and add:
- Multiply the value you just brought down by the root of the divisor, [tex]\(-1\)[/tex], and write it under the next coefficient. So, [tex]\(1 \times (-1) = -1\)[/tex].
- Add this result to the next coefficient: [tex]\(4 + (-1) = 3\)[/tex].
5. Repeat the process:
- Multiply the result from the previous step by the root of the divisor: [tex]\(3 \times (-1) = -3\)[/tex].
- Add this to the next coefficient: [tex]\(6 + (-3) = 3\)[/tex].
The final number you get after the last addition step is the remainder of the division.
In this case, the remainder is [tex]\(3\)[/tex].
Therefore, the remainder of the synthetic division is 3, which corresponds to:
D. 3
We are given the coefficients of a polynomial: [tex]\(1, 4, 6\)[/tex]. These correspond to the polynomial [tex]\(f(x) = 1x^2 + 4x + 6\)[/tex].
The divisor root, based on the setup of the problem, is [tex]\(-1\)[/tex]. This means we are dividing the polynomial by [tex]\(x + 1\)[/tex].
Synthetic Division Steps:
1. Set up the synthetic division: Write the coefficients of the polynomial in a row: [tex]\(1, 4, 6\)[/tex].
2. Write the root of the divisor (opposite sign of the given value): Since [tex]\(x + 1\)[/tex] is the divisor, we use [tex]\(-1\)[/tex].
3. Bring down the leading coefficient: Start by bringing down the first coefficient [tex]\(1\)[/tex] as is. It represents the new leading coefficient after division.
4. Multiply and add:
- Multiply the value you just brought down by the root of the divisor, [tex]\(-1\)[/tex], and write it under the next coefficient. So, [tex]\(1 \times (-1) = -1\)[/tex].
- Add this result to the next coefficient: [tex]\(4 + (-1) = 3\)[/tex].
5. Repeat the process:
- Multiply the result from the previous step by the root of the divisor: [tex]\(3 \times (-1) = -3\)[/tex].
- Add this to the next coefficient: [tex]\(6 + (-3) = 3\)[/tex].
The final number you get after the last addition step is the remainder of the division.
In this case, the remainder is [tex]\(3\)[/tex].
Therefore, the remainder of the synthetic division is 3, which corresponds to:
D. 3
