# The polynomial which when divided by – x2 + x – 1 gives a quotient x – 2 and remainder 3, isA. x3 – 3x2 + 3x – 5B. – x3 – 3x2 – 3x – 5C. – x3 + 3x2 – 3x + 5D. x3 – 3x2 – 3x + 5

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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