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If the polynomial $6 x 4 + 8 x 3 + 17 x 2 + 21 x + 7$ is divided by another polynomial $3 x 2 + 4 x + 1,$ the remainder comes out to be $(a x + b)$ . Find $a$ and $b .$

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a=4, b=3

a=2, b=1

a=3, b=4

a=1, b=2

answer is A.

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Detailed Solution

Given polynomial

6 x 4 + 8 x 3 + 17 x 2 + 21 x + 7

is divided by

3 x 2 + 4 x + 1

and the remainder obtained is

(a x + b)

. We need to find the value of

a

and

b .

.
Let us perform the long division algorithm, therefore, we have,
Question Image

The remainder comes to be

x + 2

.
But in the question it is provided that the remainder is

a x + b .

Therefore, we have,

x + 2 = a x + b

On comparing we get,

x = a x ⇒ a = 1

and

b = 2

Hence, the value of

a

1

and

b

2

.
Therefore, option 1 is correct.

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