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Answer :
Sure! Let's go through the process of synthetic division step-by-step for the given problem.
We want to divide the polynomial [tex]\(2x + 7\)[/tex] by [tex]\(x + 1\)[/tex]. Here, synthetic division can be used since we are dividing by a linear polynomial.
### Step-by-Step Solution:
1. Identify the Coefficients:
- The polynomial we are dividing is [tex]\(2x + 7\)[/tex].
- The coefficients are 2 and 7.
2. Set Up for Synthetic Division:
- Since we are dividing by [tex]\(x + 1\)[/tex], we use the root, which is [tex]\(-1\)[/tex] for synthetic division.
3. Perform Synthetic Division:
- Write down the first coefficient (2), which is the leading coefficient of the dividend, as is under the division bar.
- Multiply this number by the root (-1) and add it to the next coefficient:
- Multiply: [tex]\(2 \times (-1) = -2\)[/tex].
- Add to the next coefficient: [tex]\(-2 + 7 = 5\)[/tex].
4. Form the Quotient:
- The numbers you have after synthetic division represent the coefficients of the quotient polynomial.
- The quotient we get is [tex]\(2x + 5\)[/tex].
Therefore, when you divide [tex]\(2x + 7\)[/tex] by [tex]\(x + 1\)[/tex], your quotient in polynomial form is [tex]\(\boxed{2x + 5}\)[/tex].
The correct choice from the options given is B. [tex]\(2x + 5\)[/tex].
We want to divide the polynomial [tex]\(2x + 7\)[/tex] by [tex]\(x + 1\)[/tex]. Here, synthetic division can be used since we are dividing by a linear polynomial.
### Step-by-Step Solution:
1. Identify the Coefficients:
- The polynomial we are dividing is [tex]\(2x + 7\)[/tex].
- The coefficients are 2 and 7.
2. Set Up for Synthetic Division:
- Since we are dividing by [tex]\(x + 1\)[/tex], we use the root, which is [tex]\(-1\)[/tex] for synthetic division.
3. Perform Synthetic Division:
- Write down the first coefficient (2), which is the leading coefficient of the dividend, as is under the division bar.
- Multiply this number by the root (-1) and add it to the next coefficient:
- Multiply: [tex]\(2 \times (-1) = -2\)[/tex].
- Add to the next coefficient: [tex]\(-2 + 7 = 5\)[/tex].
4. Form the Quotient:
- The numbers you have after synthetic division represent the coefficients of the quotient polynomial.
- The quotient we get is [tex]\(2x + 5\)[/tex].
Therefore, when you divide [tex]\(2x + 7\)[/tex] by [tex]\(x + 1\)[/tex], your quotient in polynomial form is [tex]\(\boxed{2x + 5}\)[/tex].
The correct choice from the options given is B. [tex]\(2x + 5\)[/tex].
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