Answer :
To find the remainder using synthetic division, follow these steps:
1. Set up the synthetic division problem:
- The divisor is [tex]\( -2 \)[/tex].
- The polynomial's coefficients are: [tex]\( 2 \)[/tex], [tex]\( -3 \)[/tex], and [tex]\( 1 \)[/tex].
2. Write the coefficients of the polynomial:
- [tex]\( 2 \)[/tex], [tex]\( -3 \)[/tex], and [tex]\( 1 \)[/tex].
3. Perform the synthetic division:
- Bring down the first coefficient, which is [tex]\( 2 \)[/tex].
4. Multiply and add:
- Multiply the brought down number [tex]\( 2 \)[/tex] by the divisor [tex]\( -2 \)[/tex]. This gives [tex]\( -4 \)[/tex].
- Add this result to the next coefficient: [tex]\( -3 + (-4) = -7 \)[/tex].
5. Repeat the process:
- Multiply the result [tex]\( -7 \)[/tex] by [tex]\( -2 \)[/tex]. This gives [tex]\( 14 \)[/tex].
- Add this to the next coefficient: [tex]\( 1 + 14 = 15 \)[/tex].
6. Determine the remainder:
- The last number you get, [tex]\( 15 \)[/tex], is the remainder.
So, the remainder of the division is 15. Unfortunately, none of the options provided (A. 13, B. 7, C. 11, D. 9) match this result. Please double-check the problem setup or the provided options.
1. Set up the synthetic division problem:
- The divisor is [tex]\( -2 \)[/tex].
- The polynomial's coefficients are: [tex]\( 2 \)[/tex], [tex]\( -3 \)[/tex], and [tex]\( 1 \)[/tex].
2. Write the coefficients of the polynomial:
- [tex]\( 2 \)[/tex], [tex]\( -3 \)[/tex], and [tex]\( 1 \)[/tex].
3. Perform the synthetic division:
- Bring down the first coefficient, which is [tex]\( 2 \)[/tex].
4. Multiply and add:
- Multiply the brought down number [tex]\( 2 \)[/tex] by the divisor [tex]\( -2 \)[/tex]. This gives [tex]\( -4 \)[/tex].
- Add this result to the next coefficient: [tex]\( -3 + (-4) = -7 \)[/tex].
5. Repeat the process:
- Multiply the result [tex]\( -7 \)[/tex] by [tex]\( -2 \)[/tex]. This gives [tex]\( 14 \)[/tex].
- Add this to the next coefficient: [tex]\( 1 + 14 = 15 \)[/tex].
6. Determine the remainder:
- The last number you get, [tex]\( 15 \)[/tex], is the remainder.
So, the remainder of the division is 15. Unfortunately, none of the options provided (A. 13, B. 7, C. 11, D. 9) match this result. Please double-check the problem setup or the provided options.
