Question

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

(A)  2 

(B)  1 

(C)  0 

(D)  None of these

Answer 1

Correct option  (B) 1 

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. 

Therefore, remainder = 1