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Question -

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 -

(c) Divisor = – x2 + x – 1, Quotient= x – 2 and
Remainder = 3, Therefore
Polynomial = Divisor x Quotient+Remainder
= (-x2 + x – 1) (x – 2) +3
= – x3 + x2 – x + 2x2 – 2x + 2 + 3
= – x3 + 3x2 – 3x + 5

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