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When the polynomial $p (x) = x^{3} - 2 x^{2} + 3 x + 1$ is divided by $(x + 1),$ then what is the remainder obtained?

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-1

-2

answer is B.

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Detailed Solution

It is given that the polynomial

p (x) = x^{3} - 2 x^{2} + 3 x + 1

is divided by

(x + 1) .

We know by Factor theorem that if

(x - k)

is a factor of the given polynomial

p (x)

, then

p (k) = 0

and if it is not a factor then

p (k) = Remainder .

Therefore we have,

p (- 1) = {(- 1)}^{3} + 2 {(- 1)}^{2} + 3 (- 1) + 1

Therefore, the remainder is -1.
Hence, option (2) is correct.

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