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Answer :
Certainly! Let's solve the problem step-by-step using synthetic division.
For synthetic division, we're typically dividing a polynomial by a binomial of the form [tex]\( x - c \)[/tex]. The question mentions coefficients of a polynomial, which appears to be:
[tex]\[ 1x^3 + 2x^2 - 3x + 3 \][/tex]
Assuming the divisor is [tex]\( x - 1 \)[/tex] (since the problem hints at using 1), we can proceed with synthetic division as follows:
1. Setup: Write down the coefficients of the polynomial: [tex]\( [1, 2, -3, 3] \)[/tex].
2. c value: Use [tex]\( c = 1 \)[/tex] because we're dividing by [tex]\( x - 1 \)[/tex].
3. Process:
- Bring down the leading coefficient (1).
- Multiply it by [tex]\( c \)[/tex] (which is 1) and add it to the next coefficient.
- Continue this process for all coefficients.
#### Steps:
- First Column:
Bring down the first coefficient: 1.
- Second Column:
Multiply the 1 from the previous step by c (1): [tex]\(1 \times 1 = 1\)[/tex].
Add this result to the next coefficient (2): [tex]\(2 + 1 = 3\)[/tex].
- Third Column:
Multiply the 3 from the previous step by c (1): [tex]\(3 \times 1 = 3\)[/tex].
Add this result to the next coefficient (-3): [tex]\(-3 + 3 = 0\)[/tex].
- Fourth Column:
Multiply the 0 from the previous step by c (1): [tex]\(0 \times 1 = 0\)[/tex].
* Add this result to the next coefficient (3): [tex]\(3 + 0 = 3\)[/tex].
The last number in this sequence, 3, is the remainder.
So, the remainder when dividing by [tex]\( x - 1 \)[/tex] is 3.
Therefore, the answer is D. 3.
For synthetic division, we're typically dividing a polynomial by a binomial of the form [tex]\( x - c \)[/tex]. The question mentions coefficients of a polynomial, which appears to be:
[tex]\[ 1x^3 + 2x^2 - 3x + 3 \][/tex]
Assuming the divisor is [tex]\( x - 1 \)[/tex] (since the problem hints at using 1), we can proceed with synthetic division as follows:
1. Setup: Write down the coefficients of the polynomial: [tex]\( [1, 2, -3, 3] \)[/tex].
2. c value: Use [tex]\( c = 1 \)[/tex] because we're dividing by [tex]\( x - 1 \)[/tex].
3. Process:
- Bring down the leading coefficient (1).
- Multiply it by [tex]\( c \)[/tex] (which is 1) and add it to the next coefficient.
- Continue this process for all coefficients.
#### Steps:
- First Column:
Bring down the first coefficient: 1.
- Second Column:
Multiply the 1 from the previous step by c (1): [tex]\(1 \times 1 = 1\)[/tex].
Add this result to the next coefficient (2): [tex]\(2 + 1 = 3\)[/tex].
- Third Column:
Multiply the 3 from the previous step by c (1): [tex]\(3 \times 1 = 3\)[/tex].
Add this result to the next coefficient (-3): [tex]\(-3 + 3 = 0\)[/tex].
- Fourth Column:
Multiply the 0 from the previous step by c (1): [tex]\(0 \times 1 = 0\)[/tex].
* Add this result to the next coefficient (3): [tex]\(3 + 0 = 3\)[/tex].
The last number in this sequence, 3, is the remainder.
So, the remainder when dividing by [tex]\( x - 1 \)[/tex] is 3.
Therefore, the answer is D. 3.
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