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Question
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
Options
x3 − 3x2 + 3x − 5
−x3 − 3x2 − 3x − 5
−x3 + 3x2 − 3x + 5
x3 − 3x2 − 3x + 5
Solution
We know that
`f(x)= g (x)q(x)+ r(x)`
`= (- x^2 + x -1)(x - 2 + 3)`
`= - x^3 + x^2 - x+ 2x^2 - 2x + 2 + 3`
`= - x^3 + x^2 - 2x^2 - x - 2x + 2 + 3`
` = - x^3 + 3x^2 - 3x + 5`Therefore,
The polynomial which when divided by `- x^2 + x -1` gives a quotient `x -2` and remainder 3, is`- x^2 + 3x^2 - 3x + 5`
Hence, the correct choice is `(c).`
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