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Question

# 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
2x
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B
2x1
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C
3x+4
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D
x2
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Solution

## The correct option is D x−2According to division algorithm Dividend = Divisor × Quotient + Remainderp(x)=g(x)×q(x)+r(x)Putting the value in formula we get ,−x3+3x2−3x+5=(x−1−x2)×q(x)+3⇒−x3+3x2−3x+5−3=(x−1−x2)×q(x)⇒−x3+3x2−3x+2=(x−1−x2)×q(x)⇒(−x3+3x2−3x+2)=q(x)×(x−1−x2)Dividing both sides by (x−1−x2), we get,(−x3+3x2−3x+2)(x−1−x2)=q(x)So, q(x)=x−2Hence, option D.

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