Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Sure, let's divide the polynomial \(-v + 11\) by \(v - 9\).
### Step-by-Step Solution:
1. Identify the terms in both the divisor and the dividend:
- Dividend (numerator): \(-v + 11\)
- Divisor (denominator): \(v - 9\)
2. Set up the division:
[tex]$[tex]$\frac{-v + 11}{v - 9}$[/tex]$[/tex]
3. Divide the first term of the numerator by the first term of the denominator:
- First term of the numerator: \(-v\)
- First term of the denominator: \(v\)
- Divide: \(\frac{-v}{v} = -1\)
4. Multiply the entire divisor by the result from Step 3:
- Result from Step 3: \(-1\)
- Multiply by the divisor:
[tex]\[ -1 \cdot (v - 9) = -v + 9 \][/tex]
5. Subtract this result from the original numerator:
- Original numerator: \(-v + 11\)
- Result from multiplication: \(-v + 9\)
[tex]\[ (-v + 11) - (-v + 9) = -v + 11 + v - 9 = 2 \][/tex]
6. Determine the quotient and the remainder from this process:
- The quotient (result from Step 3): \(-1\)
- The remainder (result from Step 5): \(2\)
So, the quotient when dividing \(-v + 11\) by \(v - 9\) is \(-1\) and the remainder is \(2\).
### Final Answer:
[tex]\[ \text{Quotient: } -1 \][/tex]
[tex]\[ \text{Remainder: } 2 \][/tex]
The division of [tex]\(-v + 11\)[/tex] by [tex]\(v - 9\)[/tex] gives a quotient of [tex]\(-1\)[/tex] and a remainder of [tex]\(2\)[/tex].
### Step-by-Step Solution:
1. Identify the terms in both the divisor and the dividend:
- Dividend (numerator): \(-v + 11\)
- Divisor (denominator): \(v - 9\)
2. Set up the division:
[tex]$[tex]$\frac{-v + 11}{v - 9}$[/tex]$[/tex]
3. Divide the first term of the numerator by the first term of the denominator:
- First term of the numerator: \(-v\)
- First term of the denominator: \(v\)
- Divide: \(\frac{-v}{v} = -1\)
4. Multiply the entire divisor by the result from Step 3:
- Result from Step 3: \(-1\)
- Multiply by the divisor:
[tex]\[ -1 \cdot (v - 9) = -v + 9 \][/tex]
5. Subtract this result from the original numerator:
- Original numerator: \(-v + 11\)
- Result from multiplication: \(-v + 9\)
[tex]\[ (-v + 11) - (-v + 9) = -v + 11 + v - 9 = 2 \][/tex]
6. Determine the quotient and the remainder from this process:
- The quotient (result from Step 3): \(-1\)
- The remainder (result from Step 5): \(2\)
So, the quotient when dividing \(-v + 11\) by \(v - 9\) is \(-1\) and the remainder is \(2\).
### Final Answer:
[tex]\[ \text{Quotient: } -1 \][/tex]
[tex]\[ \text{Remainder: } 2 \][/tex]
The division of [tex]\(-v + 11\)[/tex] by [tex]\(v - 9\)[/tex] gives a quotient of [tex]\(-1\)[/tex] and a remainder of [tex]\(2\)[/tex].
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.