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Answer :
Sure! Let's go through the steps of synthetic division to find the remainder.
We are given the polynomial coefficients [tex]\(2, 10, 1\)[/tex] and the divisor, which is [tex]\(-5\)[/tex].
Step 1: Bring down the leading coefficient.
- The first coefficient is [tex]\(2\)[/tex], so we bring it down as the start of our result.
Step 2: Multiply and add repeatedly.
1. Multiply the result from the previous step by the divisor [tex]\(-5\)[/tex], then add the next coefficient:
- Multiply [tex]\(2\)[/tex] by [tex]\(-5\)[/tex] to get [tex]\(-10\)[/tex].
- Add [tex]\(-10\)[/tex] to the next coefficient, [tex]\(10\)[/tex], resulting in [tex]\(0\)[/tex].
2. Repeat the process with the new result:
- Now multiply [tex]\(0\)[/tex] by [tex]\(-5\)[/tex] to get [tex]\(0\)[/tex].
- Add [tex]\(0\)[/tex] to the final coefficient, [tex]\(1\)[/tex], which results in [tex]\(1\)[/tex].
Conclusion:
- The final number obtained is the remainder of the division.
Therefore, the remainder represented by the synthetic division is [tex]\(1\)[/tex].
We are given the polynomial coefficients [tex]\(2, 10, 1\)[/tex] and the divisor, which is [tex]\(-5\)[/tex].
Step 1: Bring down the leading coefficient.
- The first coefficient is [tex]\(2\)[/tex], so we bring it down as the start of our result.
Step 2: Multiply and add repeatedly.
1. Multiply the result from the previous step by the divisor [tex]\(-5\)[/tex], then add the next coefficient:
- Multiply [tex]\(2\)[/tex] by [tex]\(-5\)[/tex] to get [tex]\(-10\)[/tex].
- Add [tex]\(-10\)[/tex] to the next coefficient, [tex]\(10\)[/tex], resulting in [tex]\(0\)[/tex].
2. Repeat the process with the new result:
- Now multiply [tex]\(0\)[/tex] by [tex]\(-5\)[/tex] to get [tex]\(0\)[/tex].
- Add [tex]\(0\)[/tex] to the final coefficient, [tex]\(1\)[/tex], which results in [tex]\(1\)[/tex].
Conclusion:
- The final number obtained is the remainder of the division.
Therefore, the remainder represented by the synthetic division is [tex]\(1\)[/tex].
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