The remainder when polynomial x3-a x2-6 x-a is divided by x-1 isA- 7-2 aB- 7C- 7 - aD- 7-8 a

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Remainder Theorem

The remainder...

Question

The remainder when polynomial $x^{3} - a x^{2} + 6 x - a$ is divided by $(x - 1)$ is

7 – 2a

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7 - a

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7 - 8a

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Solution

The correct option is A
7 – 2a

Let $p (x) = x^{3} - a x^{2} + 6 x - a$ .
If p(x) is divided by (x-1), then remainder is p(1).
$p (1) = (1)^{3} - a (1)^{2} + 6 (1) - a$
= $1 - a + 6 - a = 7 - 2 a .$

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Similar questions

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 $2 A + B = 0$ .

Find the remainder when $x^{3} - a x^{2} + 6 x - a$ is divided by $x - a$ .

Q. Let

R_{1}

and

R_{2}

are the remainder when the polynomials

x^{3} + 2 x^{2} - 5 a x - 7

and

x^{3} + a x^{2} - 12 x + 6

are divided by

x + 1

and

x - 2

respectively. If

2 R_{1} + R_{2} = 6

, find the value of

a

Q. Question 2
Find the remainder when

x^{3} - a x^{2} + 6 x - a

is divided by x - a.

Q. When a polynomial

f (x)

is divided by

(x - 1)

, the remainder is

5

and when it is divided by

(x - 2)

, the remainder is

7

. Find the remainder when it is divided by

(x - 1) (x - 2)

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The remainder when polynomial x3−ax2+6x−a is divided by (x−1) is

The correct option is A 7 – 2a Let p(x)=x3−ax2+6x−a. If p(x) is divided by (x-1), then remainder is p(1). p(1)=(1)3−a(1)2+6(1)−a =1−a+6−a=7−2a.

The remainder when polynomial $x^{3} - a x^{2} + 6 x - a$ is divided by $(x - 1)$ is

The correct option is A
7 – 2a

Let $p (x) = x^{3} - a x^{2} + 6 x - a$ .
If p(x) is divided by (x-1), then remainder is p(1).
$p (1) = (1)^{3} - a (1)^{2} + 6 (1) - a$
= $1 - a + 6 - a = 7 - 2 a .$