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Question -

The polynomial which when divided by тАУ x2┬а+ x тАУ 1 gives a quotient x тАУ 2 and remainder 3, is
(a) x3┬атАУ 3x2┬а+ 3x тАУ 5
(b) тАУ x3┬атАУ 3x2┬атАУ 3x тАУ 5
(c) тАУ x3┬а+ 3x2┬атАУ 3x + 5
(d) x3┬атАУ 3x2┬атАУ 3x + 5



Answer -

(c)┬аDivisor = тАУ x2┬а+ x тАУ 1, Quotient= x тАУ 2 and
Remainder = 3, Therefore
Polynomial = Divisor x Quotient+Remainder
= (-x2┬а+ x тАУ 1) (x тАУ 2) +3
= тАУ x3┬а+ x2┬атАУ x + 2x2┬атАУ 2x + 2 + 3
= тАУ x3┬а+ 3x2┬атАУ 3x + 5

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