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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.
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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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