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When the polynomial $p (x) = x 3 + a x 2 + 2 x + a$ is divided by $x + a,$ then the remainder obtained is equal to

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a

− a

2 a

answer is C.

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Detailed Solution

It is given that the polynomial

p (x) = x 3 + a x 2 + 2 x + a

is divided by

x + a .

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 .

To calculate the remainder, we have to find

p − a .

Therefore we have,

p − a = (− a) 3 + a (− a) 2 + 2 (− a) + a ⇒ p − a = − a

Therefore, the remainder obtained is

− a .

Thus, option (3) is the correct answer.

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