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Answer :
Sure! Let's go through the steps of solving the synthetic division problem: [tex]\(1 \mid 4 \quad 6 \quad -1\)[/tex].
1. Set up the synthetic division.
- The divisor is [tex]\(1\)[/tex].
- The coefficients of the polynomial are [tex]\(4, 6, -1\)[/tex].
2. Bring down the first coefficient.
- Start by writing down the first coefficient, which is [tex]\(4\)[/tex].
3. Multiply and add.
- Multiply the divisor ([tex]\(1\)[/tex]) by the number you just brought down ([tex]\(4\)[/tex]), which gives [tex]\(4\)[/tex].
- Add this result to the next coefficient:
- [tex]\(6 + 4 = 10\)[/tex].
- Write [tex]\(10\)[/tex] below the line.
4. Repeat the multiplication and addition.
- Multiply the divisor ([tex]\(1\)[/tex]) by the result you just got ([tex]\(10\)[/tex]), resulting in [tex]\(10\)[/tex].
- Add this result to the last coefficient:
- [tex]\(-1 + 10 = 9\)[/tex].
- This gives you the remainder.
So, the remainder when dividing using synthetic division is [tex]\(9\)[/tex].
Therefore, the remainder is:
[tex]\[ \boxed{9} \][/tex]
1. Set up the synthetic division.
- The divisor is [tex]\(1\)[/tex].
- The coefficients of the polynomial are [tex]\(4, 6, -1\)[/tex].
2. Bring down the first coefficient.
- Start by writing down the first coefficient, which is [tex]\(4\)[/tex].
3. Multiply and add.
- Multiply the divisor ([tex]\(1\)[/tex]) by the number you just brought down ([tex]\(4\)[/tex]), which gives [tex]\(4\)[/tex].
- Add this result to the next coefficient:
- [tex]\(6 + 4 = 10\)[/tex].
- Write [tex]\(10\)[/tex] below the line.
4. Repeat the multiplication and addition.
- Multiply the divisor ([tex]\(1\)[/tex]) by the result you just got ([tex]\(10\)[/tex]), resulting in [tex]\(10\)[/tex].
- Add this result to the last coefficient:
- [tex]\(-1 + 10 = 9\)[/tex].
- This gives you the remainder.
So, the remainder when dividing using synthetic division is [tex]\(9\)[/tex].
Therefore, the remainder is:
[tex]\[ \boxed{9} \][/tex]
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