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If the polynomial 3x2 – x3 – 3x + 5 is divided by another polynomial x – 1 – x2, the remainder comes out to be 3, then quotient polynomial is –

  • a)
    2 – x

  • b)
    2x – 1

  • c)
    3x + 4

  • d)
    x - 2

Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If the polynomial 3x2– x3– 3x + 5 is divided by another po...
Let's assume the quotient polynomial as ax + b.
Now, (x - 1 - x^2)(ax + b) + 3 = 3x^2 - x^3 - 3x + 5
ax^3 + bx^2 + ax^2 - ax^2 - bx - a + 3 = -x^3 + 3x^2 - 3x + 5
ax^3 + (b - 1)x^2 + (a - b)x + (3 - a) = -x^3 + 3x^2 - 3x + 5
Equating the coefficients of the same degree terms on both sides, we get:
For x^3: a = -1 For x^2: b - 1 = 3 => b = 4 For x: a - b = -3 => a - 4 = -3 => a = 1 For constant: 3 - a = 5 => a = -2
Therefore, the quotient polynomial is x + 4.
Hence, the quotient polynomial is x + 4.
Community Answer
If the polynomial 3x2– x3– 3x + 5 is divided by another po...
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If the polynomial 3x2– x3– 3x + 5 is divided by another polynomial x – 1 – x2, the remainder comes out to be 3, then quotient polynomial is –a)2 – xb)2x – 1c)3x + 4d)x - 2Correct answer is option 'D'. Can you explain this answer?
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If the polynomial 3x2– x3– 3x + 5 is divided by another polynomial x – 1 – x2, the remainder comes out to be 3, then quotient polynomial is –a)2 – xb)2x – 1c)3x + 4d)x - 2Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the polynomial 3x2– x3– 3x + 5 is divided by another polynomial x – 1 – x2, the remainder comes out to be 3, then quotient polynomial is –a)2 – xb)2x – 1c)3x + 4d)x - 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the polynomial 3x2– x3– 3x + 5 is divided by another polynomial x – 1 – x2, the remainder comes out to be 3, then quotient polynomial is –a)2 – xb)2x – 1c)3x + 4d)x - 2Correct answer is option 'D'. Can you explain this answer?.
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