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Answer :
To solve this synthetic division problem, let's go through the steps:
1. Identify the Divisor and Dividend:
- You need to divide the polynomial [tex]\(2x - 7\)[/tex] by the expression [tex]\(x + 1\)[/tex].
2. Set Up for Synthetic Division:
- Use the root of the divisor, which is [tex]\(-1\)[/tex] (from [tex]\(x + 1 = 0 \rightarrow x = -1\)[/tex]).
- List the coefficients of the polynomial [tex]\(2x - 7\)[/tex], which are [tex]\([2, -7]\)[/tex].
3. Perform Synthetic Division:
- Step 1: Bring down the first coefficient, which is [tex]\(2\)[/tex].
- Step 2: Multiply this number by [tex]\(-1\)[/tex] and add it to the next coefficient:
- Multiply [tex]\(2\)[/tex] by [tex]\(-1\)[/tex] to get [tex]\(-2\)[/tex].
- Add [tex]\(-2\)[/tex] to [tex]\(-7\)[/tex] to get [tex]\(-9\)[/tex].
4. Interpret the Result:
- The result of the synthetic division is [tex]\([2, -9]\)[/tex].
- This means we have a quotient of [tex]\(2x - 9\)[/tex].
5. Choose the Correct Option:
- From the choices given:
- A. [tex]\(x - 5\)[/tex]
- B. [tex]\(x + 5\)[/tex]
- C. [tex]\(2x + 5\)[/tex]
- D. [tex]\(2x - 5\)[/tex]
Since the correct quotient we found is [tex]\(2x - 9\)[/tex], it reminds us that the listed options might be incorrect.
Thus, the actual quotient from the synthetic division is not directly given as an option, which suggests there may be an error in the problem as it currently stands. The result which we calculated is [tex]\(2x - 9\)[/tex].
1. Identify the Divisor and Dividend:
- You need to divide the polynomial [tex]\(2x - 7\)[/tex] by the expression [tex]\(x + 1\)[/tex].
2. Set Up for Synthetic Division:
- Use the root of the divisor, which is [tex]\(-1\)[/tex] (from [tex]\(x + 1 = 0 \rightarrow x = -1\)[/tex]).
- List the coefficients of the polynomial [tex]\(2x - 7\)[/tex], which are [tex]\([2, -7]\)[/tex].
3. Perform Synthetic Division:
- Step 1: Bring down the first coefficient, which is [tex]\(2\)[/tex].
- Step 2: Multiply this number by [tex]\(-1\)[/tex] and add it to the next coefficient:
- Multiply [tex]\(2\)[/tex] by [tex]\(-1\)[/tex] to get [tex]\(-2\)[/tex].
- Add [tex]\(-2\)[/tex] to [tex]\(-7\)[/tex] to get [tex]\(-9\)[/tex].
4. Interpret the Result:
- The result of the synthetic division is [tex]\([2, -9]\)[/tex].
- This means we have a quotient of [tex]\(2x - 9\)[/tex].
5. Choose the Correct Option:
- From the choices given:
- A. [tex]\(x - 5\)[/tex]
- B. [tex]\(x + 5\)[/tex]
- C. [tex]\(2x + 5\)[/tex]
- D. [tex]\(2x - 5\)[/tex]
Since the correct quotient we found is [tex]\(2x - 9\)[/tex], it reminds us that the listed options might be incorrect.
Thus, the actual quotient from the synthetic division is not directly given as an option, which suggests there may be an error in the problem as it currently stands. The result which we calculated is [tex]\(2x - 9\)[/tex].
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