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Answer :
Let's solve the synthetic division problem step-by-step.
We are dividing the polynomial [tex]\(2x^2 + 5x - 1\)[/tex] by [tex]\(x - 2\)[/tex]. The synthetic division process will help us find the quotient.
1. Write down the coefficients of the dividend: The polynomial [tex]\(2x^2 + 5x - 1\)[/tex] has the coefficients [tex]\(1, 5, -1\)[/tex].
2. Set up the synthetic division scheme: Write the divisor's root [tex]\(x - 2 = 0\)[/tex], which gives us [tex]\(x = 2\)[/tex].
3. Begin the synthetic division:
- Bring down the first coefficient, which is 1. This is the leading coefficient of the quotient.
4. Multiply: Multiply the number brought down by the root [tex]\(x = 2\)[/tex] and write the result under the next coefficient:
- [tex]\(1 \times 2 = 2\)[/tex]
5. Add: Add this result to the next coefficient:
- [tex]\(5 + 2 = 7\)[/tex]
6. Repeat the process:
- Multiply the result [tex]\(7\)[/tex] by [tex]\(2\)[/tex]: [tex]\(7 \times 2 = 14\)[/tex]
- Add this to the next coefficient [tex]\(-1\)[/tex]: [tex]\(-1 + 14 = 13\)[/tex]
7. Determine the quotient and remainder:
- The coefficients you've calculated, starting from 1, are the coefficients of the quotient. So the quotient is [tex]\(x + 7\)[/tex].
- The last number (13) is the remainder.
Therefore, the quotient in polynomial form is [tex]\(x + 7\)[/tex].
The correct answer is D. [tex]\(x + 7\)[/tex].
We are dividing the polynomial [tex]\(2x^2 + 5x - 1\)[/tex] by [tex]\(x - 2\)[/tex]. The synthetic division process will help us find the quotient.
1. Write down the coefficients of the dividend: The polynomial [tex]\(2x^2 + 5x - 1\)[/tex] has the coefficients [tex]\(1, 5, -1\)[/tex].
2. Set up the synthetic division scheme: Write the divisor's root [tex]\(x - 2 = 0\)[/tex], which gives us [tex]\(x = 2\)[/tex].
3. Begin the synthetic division:
- Bring down the first coefficient, which is 1. This is the leading coefficient of the quotient.
4. Multiply: Multiply the number brought down by the root [tex]\(x = 2\)[/tex] and write the result under the next coefficient:
- [tex]\(1 \times 2 = 2\)[/tex]
5. Add: Add this result to the next coefficient:
- [tex]\(5 + 2 = 7\)[/tex]
6. Repeat the process:
- Multiply the result [tex]\(7\)[/tex] by [tex]\(2\)[/tex]: [tex]\(7 \times 2 = 14\)[/tex]
- Add this to the next coefficient [tex]\(-1\)[/tex]: [tex]\(-1 + 14 = 13\)[/tex]
7. Determine the quotient and remainder:
- The coefficients you've calculated, starting from 1, are the coefficients of the quotient. So the quotient is [tex]\(x + 7\)[/tex].
- The last number (13) is the remainder.
Therefore, the quotient in polynomial form is [tex]\(x + 7\)[/tex].
The correct answer is D. [tex]\(x + 7\)[/tex].
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