Answer :
Sure! Let's solve this synthetic division problem step-by-step:
We're given the polynomial with coefficients [tex]\(1, 2, 2, -3\)[/tex], and we need to divide this by [tex]\(x - 1\)[/tex], which means we use [tex]\(1\)[/tex] for synthetic division.
1. Set Up the Synthetic Division:
- Write down the coefficients of the polynomial: [tex]\(1, 2, 2, -3\)[/tex].
- The divisor is the number next to the long division symbol, which is [tex]\(1\)[/tex].
2. Begin the Process:
- Bring down the first coefficient [tex]\(1\)[/tex] to start the bottom row.
3. Multiply and Add:
- Multiply the divisor [tex]\(1\)[/tex] by the number you just brought down [tex]\(1\)[/tex]. This gives you [tex]\(1\)[/tex].
- Add this to the next coefficient: [tex]\(2\ + 1 = 3\)[/tex].
- Bring this result down to continue the bottom row.
4. Repeat the Multiply and Add:
- Multiply the divisor [tex]\(1\)[/tex] by the last result [tex]\(3\)[/tex]. This gives you [tex]\(3\)[/tex].
- Add this to the next coefficient: [tex]\(2\ + 3 = 5\)[/tex].
- Bring this result down to continue the bottom row.
5. Repeat Once More:
- Multiply the divisor [tex]\(1\)[/tex] by the last result [tex]\(5\)[/tex]. This gives you [tex]\(5\)[/tex].
- Add this to the last coefficient: [tex]\(-3\ + 5 = 2\)[/tex].
- Bring this result down to continue the bottom row.
6. Identify the Remainder:
- The last number in the bottom row is [tex]\(2\)[/tex], which represents the remainder of the division.
Thus, the remainder when dividing the polynomial by [tex]\(x - 1\)[/tex] is [tex]\(2\)[/tex].
Therefore, the answer is: [tex]\(2\)[/tex].
It looks like none of the given options (A. 5, B. 4, C. 6, D. 3) directly matches this remainder, so make sure there is no mistake in the options or in understanding the process; the remainder is indeed [tex]\(2\)[/tex].
We're given the polynomial with coefficients [tex]\(1, 2, 2, -3\)[/tex], and we need to divide this by [tex]\(x - 1\)[/tex], which means we use [tex]\(1\)[/tex] for synthetic division.
1. Set Up the Synthetic Division:
- Write down the coefficients of the polynomial: [tex]\(1, 2, 2, -3\)[/tex].
- The divisor is the number next to the long division symbol, which is [tex]\(1\)[/tex].
2. Begin the Process:
- Bring down the first coefficient [tex]\(1\)[/tex] to start the bottom row.
3. Multiply and Add:
- Multiply the divisor [tex]\(1\)[/tex] by the number you just brought down [tex]\(1\)[/tex]. This gives you [tex]\(1\)[/tex].
- Add this to the next coefficient: [tex]\(2\ + 1 = 3\)[/tex].
- Bring this result down to continue the bottom row.
4. Repeat the Multiply and Add:
- Multiply the divisor [tex]\(1\)[/tex] by the last result [tex]\(3\)[/tex]. This gives you [tex]\(3\)[/tex].
- Add this to the next coefficient: [tex]\(2\ + 3 = 5\)[/tex].
- Bring this result down to continue the bottom row.
5. Repeat Once More:
- Multiply the divisor [tex]\(1\)[/tex] by the last result [tex]\(5\)[/tex]. This gives you [tex]\(5\)[/tex].
- Add this to the last coefficient: [tex]\(-3\ + 5 = 2\)[/tex].
- Bring this result down to continue the bottom row.
6. Identify the Remainder:
- The last number in the bottom row is [tex]\(2\)[/tex], which represents the remainder of the division.
Thus, the remainder when dividing the polynomial by [tex]\(x - 1\)[/tex] is [tex]\(2\)[/tex].
Therefore, the answer is: [tex]\(2\)[/tex].
It looks like none of the given options (A. 5, B. 4, C. 6, D. 3) directly matches this remainder, so make sure there is no mistake in the options or in understanding the process; the remainder is indeed [tex]\(2\)[/tex].
