You visited us 1 times! Enjoying our articles? Unlock Full Access!

Remainder Theorem

Let x2+x+1 is...

Question

Let $x^{2} + x + 1$ is divisible by $3$ . If $x$ is divided by $3$ , the remainder will be

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $1$
Given: $x^{2} + x + 1$ is divisible by $3$ .

Case $I :$ $x = 3 m$

$∴ 9 m^{2} + 3 m + 1$

$∴$ Not divisible by $3$ .

Case $I I :$ $x = 3 m + 1$

$∴ 9 m^{2} + 9 m + 3$

$∴$ Divisible by $3$ .

Case $I I I :$ $x = 3 m + 2$

$∴ 9 m^{2} + 15 m + 7$

$∴$ Not divisible by $3$ .

If $x^{2} + x + 1$ is divisible by $3$ , $x = 3 m + 1$

$∴$ Remainder $= 1$

Suggest Corrections

Similar questions

Q. Let

x^{2} + x + 1

is divisible by 3. If

x

is divided by 3, the remainder will be

Q. Let

f (x) = a x^{3} + 5 x^{2} - b x + 1.

f (x)

leaves remainder

5

, when divided by

2 x + 1

, and

f^{'} (x)

is divisible by

3 x - 1

, then

if a polynomial is divided by (x-2) itr leaves remainder 1. if it is divided by (x-3) it leaves remainder 3.what will be the remainder of the same polynomial when divided by (x-2)(x-3)

Q. Let

f (x) = x^{2} + 3 x + 2

. Then the remainder when

f (x)

is divided by

(x - 1)

will be :

Q. If a polynomial

f (x)

is divided by

x^{2} - 16

then remainder is

5 x + 3

, what will be the remainder when the same polynomial is divided by

(x + 4)

Join BYJU'S Learning Program

Let x2+x+1 is divisible by 3. If x is divided by 3, the remainder will be

The correct option is D 1Given: x2+x+1 is divisible by 3. Case I: x=3m ∴9m2+3m+1 ∴ Not divisible by 3. Case II: x=3m+1 ∴9m2+9m+3 ∴ Divisible by 3. Case III: x=3m+2 ∴9m2+15m+7 ∴ Not divisible by 3. If x2+x+1 is divisible by 3, x=3m+1 ∴ Remainder =1

Let $x^{2} + x + 1$ is divisible by $3$ . If $x$ is divided by $3$ , the remainder will be