When the polynomial $(6 x^{4} + 8 x^{3} + 17 x^{2} + 21 x + 7)$ is divided by $(3 x^{2} + 4 x + 1)$ the remainder is (ax - b) Therefore

a = 1, b = 2

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a = 1, b= - 2

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a = 2, b = 1

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a = -1, b = -2

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Solution

The correct option is A a = 1, b= - 2
$3 x^{2} + 4 x + 1) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 6 x^{4} + 8 x^{3} + 17 x^{2} + 21 x + 7 (2 x^{2} + 5$
$6 x^{4} - + 8 x^{3} - + - 2 x^{2} - -------------- -$
$15 x^{2} + 21 x + 7$
$15 x^{2} - + 20 x - + 5 - - ------------ -$
$x + 2$
Hence remainder is $x + 2$ .
On comparing $x + 2$ with $a x - b$ , we get
$a = 1, b = - 2$
Option B is correct.

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Similar questions

Q. 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.
[4 MARKS]

Q. If the polynomial

f (x) = (6 x^{4} + 8 x^{2} + 17 x^{2} + 21 x + 7)

is divided by another polynomial

g (x) = 3 x^{2} + 4 x + 1

the remainder is

(a x + b)

. Find

a

and

b

When the polynomial $x^{3} + 2 x^{2} - 5 a x - 7$ is divided by $(x - 1)$ , the remainder is A and when the polynomial $x^{3} + a x^{2} - 12 x + 16$ is divided by $(x + 2)$ , the remainder is B. Find the value of 'a' if $2 A + B = 0$ .

Q. The polynomial f(x) = x⁴ − 2x³ + 3x² − ax = b when divided by (x − 1) and (x + 1) leaves the remainder 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when f(x) is divided by (x − 2).

The polynomial $p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b$ when divided by (x-1) and (x +1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when p(x) is divided by (x -2).

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When the polynomial (6x4+8x3+17x2+21x+7) is divided by (3x2+4x+1) the remainder is (ax - b) Therefore

When the polynomial $(6 x^{4} + 8 x^{3} + 17 x^{2} + 21 x + 7)$ is divided by $(3 x^{2} + 4 x + 1)$ the remainder is (ax - b) Therefore