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When the polynomial $p (x) = 4 x 3 − 12 x 2 + 11 x − 5$ is divided by $2 x − 1,$ then the remainder obtained is:

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-2

-1

answer is B.

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Detailed Solution

It is given that the polynomial

p (x) = 4 x 3 − 12 x 2 + 11 x − 5

is divided by

2 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 .

Equate

2 x − 1 = 0.

⇒ x = 12

To calculate the remainder, we have to find the value of

p 12 .

⇒ p 12 = 4123 − 12122 + 1112 − 5 ⇒ p 12 = 12 − 3 + 112 − 5 ⇒ p 12 = − 42 ⇒ p 12 = − 2

Therefore, the remainder obtained is -2.
Thus, option (2) is the correct answer.

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