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By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x6 1; x2 –1?
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By actual division, find the quotient and the remainder when the first...
Polynomial Division: x6 - 1 ÷ x2 - 1
To divide the polynomial x6 - 1 by x2 - 1, we will perform long division.
- **Step 1: Division of leading terms**
Divide the leading term of the dividend by the leading term of the divisor.
x6 ÷ x2 = x4
- **Step 2: Multiply and subtract**
Multiply the divisor x2 - 1 by x4 to get x6 - x4. Subtract this from the dividend.
x6 - (x6 - x4) = x4
- **Step 3: Bring down the next term**
Bring down the next term from the dividend.
x4 - 1
- **Step 4: Division of leading terms**
Divide the leading term of the new dividend x4 by the leading term of the divisor x2.
x4 ÷ x2 = x2
- **Step 5: Multiply and subtract**
Multiply the divisor x2 - 1 by x2 to get x4 - x2. Subtract this from the new dividend.
x4 - (x4 - x2) = x2
- **Step 6: Division of leading terms**
Divide the leading term of the new dividend x2 by the leading term of the divisor x2.
x2 ÷ x2 = 1
Since the degree of the new dividend is less than the degree of the divisor, we stop the division process.
Therefore, the quotient is x4 + x2 + 1 and the remainder is 0.
To divide the polynomial x6 - 1 by x2 - 1, we will perform long division.
- **Step 1: Division of leading terms**
Divide the leading term of the dividend by the leading term of the divisor.
x6 ÷ x2 = x4
- **Step 2: Multiply and subtract**
Multiply the divisor x2 - 1 by x4 to get x6 - x4. Subtract this from the dividend.
x6 - (x6 - x4) = x4
- **Step 3: Bring down the next term**
Bring down the next term from the dividend.
x4 - 1
- **Step 4: Division of leading terms**
Divide the leading term of the new dividend x4 by the leading term of the divisor x2.
x4 ÷ x2 = x2
- **Step 5: Multiply and subtract**
Multiply the divisor x2 - 1 by x2 to get x4 - x2. Subtract this from the new dividend.
x4 - (x4 - x2) = x2
- **Step 6: Division of leading terms**
Divide the leading term of the new dividend x2 by the leading term of the divisor x2.
x2 ÷ x2 = 1
Since the degree of the new dividend is less than the degree of the divisor, we stop the division process.
Therefore, the quotient is x4 + x2 + 1 and the remainder is 0.
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By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x6 1; x2 –1?
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By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x6 1; x2 –1? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x6 1; x2 –1? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x6 1; x2 –1?.
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x6 1; x2 –1? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x6 1; x2 –1? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x6 1; x2 –1?.
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