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Answer :
Sure! To find the remainder in a synthetic division problem, follow these steps:
1. Identify the Dividend and Divisor:
- The dividend is given by the coefficients of the polynomial: [tex]\(1, 2, -3, 1\)[/tex].
- The divisor in the form [tex]\(x - c\)[/tex] has [tex]\(c = -2\)[/tex].
2. Setup for Synthetic Division:
- Write down the coefficients of the dividend: [tex]\(1, 2, -3, 1\)[/tex].
- To the left, write the value to be used in synthetic division, which is [tex]\(c = -2\)[/tex].
3. Synthetic Division Process:
- Bring down the leading coefficient (1) to start the calculation below the line.
- Multiply this number by [tex]\(c = -2\)[/tex] and write the result under the next coefficient.
- Add this result to the next coefficient and write the sum below the line.
- Repeat this multiply and add process for each coefficient.
Here is a step-by-step breakdown:
- Step 1: Bring down the first coefficient, 1.
[tex]\[
\text{Row below: } 1
\][/tex]
- Step 2: Multiply 1 by -2 (gives -2), add to 2 (next coefficient).
[tex]\[
2 + (-2) = 0
\][/tex]
- Step 3: Multiply 0 by -2 (gives 0), add to -3.
[tex]\[
-3 + 0 = -3
\][/tex]
- Step 4: Multiply -3 by -2 (gives 6), add to 1.
[tex]\[
1 + 6 = 7
\][/tex]
4. Result:
- The last number you get is the remainder. In this case, the remainder is [tex]\(7\)[/tex].
So, the remainder in the synthetic division problem is [tex]\(7\)[/tex]. The correct choice is C.
1. Identify the Dividend and Divisor:
- The dividend is given by the coefficients of the polynomial: [tex]\(1, 2, -3, 1\)[/tex].
- The divisor in the form [tex]\(x - c\)[/tex] has [tex]\(c = -2\)[/tex].
2. Setup for Synthetic Division:
- Write down the coefficients of the dividend: [tex]\(1, 2, -3, 1\)[/tex].
- To the left, write the value to be used in synthetic division, which is [tex]\(c = -2\)[/tex].
3. Synthetic Division Process:
- Bring down the leading coefficient (1) to start the calculation below the line.
- Multiply this number by [tex]\(c = -2\)[/tex] and write the result under the next coefficient.
- Add this result to the next coefficient and write the sum below the line.
- Repeat this multiply and add process for each coefficient.
Here is a step-by-step breakdown:
- Step 1: Bring down the first coefficient, 1.
[tex]\[
\text{Row below: } 1
\][/tex]
- Step 2: Multiply 1 by -2 (gives -2), add to 2 (next coefficient).
[tex]\[
2 + (-2) = 0
\][/tex]
- Step 3: Multiply 0 by -2 (gives 0), add to -3.
[tex]\[
-3 + 0 = -3
\][/tex]
- Step 4: Multiply -3 by -2 (gives 6), add to 1.
[tex]\[
1 + 6 = 7
\][/tex]
4. Result:
- The last number you get is the remainder. In this case, the remainder is [tex]\(7\)[/tex].
So, the remainder in the synthetic division problem is [tex]\(7\)[/tex]. The correct choice is C.
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