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