The polynomial which when divided by – x^{2} + x – 1 gives a quotient x – 2 and remainder 3, is

Given,

Divisor = – x^{2} + x – 1

Quotient = x – 2

Remainder = 3

Now we have to find out Dividend…

As we know that,

Dividend = Divisor × Quotient + Remainder

Dividend = ( – x^{2} + x – 1)(x – 2) + 3

= – x^{3} + x^{2} – x + 2x^{2} – 2x + 2 + 3

= – x^{3} + 3x^{2} – 3x + 5

So,

The required polynomial is – x^{3} + 3x^{2} – 3x + 5

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