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Answer :
Sure! Let's solve the synthetic division problem step-by-step:
### Problem:
We are given the polynomial with coefficients [tex]\(1, 5, -14\)[/tex] and we need to perform synthetic division by 2. Then, we find the quotient in polynomial form.
### Steps for Synthetic Division:
1. Initialize Setup:
- Start with the first coefficient, which is [tex]\(1\)[/tex].
2. Step-by-Step Division:
- First Column:
- Bring down the first coefficient [tex]\(1\)[/tex]. This becomes the first coefficient of the quotient.
- Second Column:
- Multiply the number you just brought down (1) by the divisor (2): [tex]\(1 \times 2 = 2\)[/tex].
- Add this to the next coefficient: [tex]\(5 + 2 = 7\)[/tex].
- This becomes the second coefficient of the quotient.
3. Quotient:
- After performing these steps, we have coefficients [tex]\(1\)[/tex] and [tex]\(7\)[/tex].
### Conclusion:
The quotient of the polynomial after performing the synthetic division is represented by the coefficients [tex]\([1, 7]\)[/tex]. This means the quotient is:
[tex]\[ x + 7 \][/tex]
So, the correct answer corresponds to:
B. [tex]\(x + 7\)[/tex]
### Problem:
We are given the polynomial with coefficients [tex]\(1, 5, -14\)[/tex] and we need to perform synthetic division by 2. Then, we find the quotient in polynomial form.
### Steps for Synthetic Division:
1. Initialize Setup:
- Start with the first coefficient, which is [tex]\(1\)[/tex].
2. Step-by-Step Division:
- First Column:
- Bring down the first coefficient [tex]\(1\)[/tex]. This becomes the first coefficient of the quotient.
- Second Column:
- Multiply the number you just brought down (1) by the divisor (2): [tex]\(1 \times 2 = 2\)[/tex].
- Add this to the next coefficient: [tex]\(5 + 2 = 7\)[/tex].
- This becomes the second coefficient of the quotient.
3. Quotient:
- After performing these steps, we have coefficients [tex]\(1\)[/tex] and [tex]\(7\)[/tex].
### Conclusion:
The quotient of the polynomial after performing the synthetic division is represented by the coefficients [tex]\([1, 7]\)[/tex]. This means the quotient is:
[tex]\[ x + 7 \][/tex]
So, the correct answer corresponds to:
B. [tex]\(x + 7\)[/tex]
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