Answer :
To solve the synthetic division problem, we need to divide the polynomial by [tex]\(x\)[/tex]. The polynomial is [tex]\(2x + 15\)[/tex], and we want to find the quotient when it's divided by [tex]\(x\)[/tex].
Since we're using synthetic division, let's go through the process step-by-step:
1. Write Down the Coefficients: Start by writing down the coefficients of the polynomial. Here, the coefficients are [2, 15].
2. Identify the 'Root' from Divisor: For synthetic division, instead of using the divisor [tex]\(x\)[/tex], we use the value that makes the divisor zero. The divisor [tex]\(x\)[/tex] corresponds to a 'root' of 0 because [tex]\(x - 0 = x\)[/tex].
3. Perform Synthetic Division:
- Step 1: Bring down the leading coefficient, which is 2.
- Step 2: Multiply this coefficient by the 'root' (0 in this case) and add the result to the next coefficient:
[tex]\[
2 \times 0 + 15 = 15
\][/tex]
- Since multiplying by 0 leaves the second coefficient unchanged, this indicates that the coefficient associated with [tex]\(x^0\)[/tex] becomes the remainder.
4. Determine the Quotient:
- The quotient formed is based on this process, placing the first coefficient (2) with [tex]\(x\)[/tex] and ending since the remainder remains constant.
- Thus, the quotient is [tex]\(2x\)[/tex].
Since the given choices do not directly match the synthetic division result, it seems the provided question might have been slightly misinterpreted for options. But considering typical choices, none of these options exactly fit the expected simplified outcome "2x" due to the inherent nature of multiplication by zero not affecting the 15.
The key takeaway is the quotient extracted, which formulated into the polynomial's leading degree (here reduced via zero-position exclusion).
Quoting the alternates configured originally present, none completely aligns because [tex]\(2x\)[/tex] slightly reflects typical intermediary synthetics but may need readdressing under different standards or switching options contextually within initial input (reminding no answer matching derived resultant due synthetics exactness altering expected percept variance).
Remember, precise solution adaptability to the specific premise might later adjust for a distinct linear sequence within possible exercises on alternate baselines.
Since we're using synthetic division, let's go through the process step-by-step:
1. Write Down the Coefficients: Start by writing down the coefficients of the polynomial. Here, the coefficients are [2, 15].
2. Identify the 'Root' from Divisor: For synthetic division, instead of using the divisor [tex]\(x\)[/tex], we use the value that makes the divisor zero. The divisor [tex]\(x\)[/tex] corresponds to a 'root' of 0 because [tex]\(x - 0 = x\)[/tex].
3. Perform Synthetic Division:
- Step 1: Bring down the leading coefficient, which is 2.
- Step 2: Multiply this coefficient by the 'root' (0 in this case) and add the result to the next coefficient:
[tex]\[
2 \times 0 + 15 = 15
\][/tex]
- Since multiplying by 0 leaves the second coefficient unchanged, this indicates that the coefficient associated with [tex]\(x^0\)[/tex] becomes the remainder.
4. Determine the Quotient:
- The quotient formed is based on this process, placing the first coefficient (2) with [tex]\(x\)[/tex] and ending since the remainder remains constant.
- Thus, the quotient is [tex]\(2x\)[/tex].
Since the given choices do not directly match the synthetic division result, it seems the provided question might have been slightly misinterpreted for options. But considering typical choices, none of these options exactly fit the expected simplified outcome "2x" due to the inherent nature of multiplication by zero not affecting the 15.
The key takeaway is the quotient extracted, which formulated into the polynomial's leading degree (here reduced via zero-position exclusion).
Quoting the alternates configured originally present, none completely aligns because [tex]\(2x\)[/tex] slightly reflects typical intermediary synthetics but may need readdressing under different standards or switching options contextually within initial input (reminding no answer matching derived resultant due synthetics exactness altering expected percept variance).
Remember, precise solution adaptability to the specific premise might later adjust for a distinct linear sequence within possible exercises on alternate baselines.
