Answer :
Sure! Let's tackle the synthetic division problem step-by-step to find the remainder.
We are given the polynomial coefficients as [tex]\(1, 2, -3, 2\)[/tex] and need to perform synthetic division by the number represented in the problem, which is [tex]\(1\)[/tex].
Here’s how synthetic division works:
1. Write down the coefficients of the polynomial: [tex]\(1, 2, -3, 2\)[/tex].
2. Set up the synthetic division by writing down the divisor. Here, the divisor is [tex]\(1\)[/tex].
3. Bring down the first coefficient, which is [tex]\(1\)[/tex].
4. Multiply this number by the divisor ([tex]\(1\)[/tex]), which gives [tex]\(1\)[/tex], and add it to the next coefficient ([tex]\(2\)[/tex]):
[tex]\[
1 \times 1 + 2 = 3
\][/tex]
5. Repeat this process:
- Multiply [tex]\(3\)[/tex] (the result from the previous step) by the divisor ([tex]\(1\)[/tex]) to get [tex]\(3\)[/tex], and add it to the next coefficient (-3):
[tex]\[
3 \times 1 + (-3) = 0
\][/tex]
- Next, take the result [tex]\(0\)[/tex], multiply it by the divisor [tex]\(1\)[/tex] to get [tex]\(0\)[/tex], and add it to the last coefficient ([tex]\(2\)[/tex]):
[tex]\[
0 \times 1 + 2 = 2
\][/tex]
6. The remainder is the last number you get after performing these operations. In this case, the remainder is [tex]\(2\)[/tex].
Thus, the answer to the synthetic division problem is:
D. 2
We are given the polynomial coefficients as [tex]\(1, 2, -3, 2\)[/tex] and need to perform synthetic division by the number represented in the problem, which is [tex]\(1\)[/tex].
Here’s how synthetic division works:
1. Write down the coefficients of the polynomial: [tex]\(1, 2, -3, 2\)[/tex].
2. Set up the synthetic division by writing down the divisor. Here, the divisor is [tex]\(1\)[/tex].
3. Bring down the first coefficient, which is [tex]\(1\)[/tex].
4. Multiply this number by the divisor ([tex]\(1\)[/tex]), which gives [tex]\(1\)[/tex], and add it to the next coefficient ([tex]\(2\)[/tex]):
[tex]\[
1 \times 1 + 2 = 3
\][/tex]
5. Repeat this process:
- Multiply [tex]\(3\)[/tex] (the result from the previous step) by the divisor ([tex]\(1\)[/tex]) to get [tex]\(3\)[/tex], and add it to the next coefficient (-3):
[tex]\[
3 \times 1 + (-3) = 0
\][/tex]
- Next, take the result [tex]\(0\)[/tex], multiply it by the divisor [tex]\(1\)[/tex] to get [tex]\(0\)[/tex], and add it to the last coefficient ([tex]\(2\)[/tex]):
[tex]\[
0 \times 1 + 2 = 2
\][/tex]
6. The remainder is the last number you get after performing these operations. In this case, the remainder is [tex]\(2\)[/tex].
Thus, the answer to the synthetic division problem is:
D. 2
