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) 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