Q. 304.5( 4 Votes )

The polynomial which when divided by – x2 + x – 1 gives a quotient x – 2 and remainder 3, is
A. x3 – 3x2 + 3x – 5

B. – x3 – 3x2 – 3x – 5

C. – x3 + 3x2 – 3x + 5

D. x3 – 3x2 – 3x + 5

Answer :

Given,


Divisor = – x2 + x – 1


Quotient = x – 2


Remainder = 3


Now we have to find out Dividend…


As we know that,


Dividend = Divisor × Quotient + Remainder


Dividend = ( – x2 + x – 1)(x – 2) + 3


= – x3 + x2 – x + 2x2 – 2x + 2 + 3


= – x3 + 3x2 – 3x + 5


So,


The required polynomial is – x3 + 3x2 – 3x + 5

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