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When the polynomial $p (x) = 81 x 4 + 54 x 3 − 9 x 2 − 3 x + 2$ is divided by $3 x + 2,$ then what is the remainder obtained?

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-1

answer is A.

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Detailed Solution

It is given that the polynomial

p (x) = 81 x 4 + 54 x 3 − 9 x 2 − 3 x + 2

is divided by

3 x + 2.

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 .

Equate

3 x + 2 = 0.

⇒ x = − 2 3

Now, to find the remainder, we have to find the value of

p − 2 3 .

Therefore, the remainder is 0.
Thus, option (1) is the correct answer.

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