Question

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

• A. 2
• B. 1
• C. 0
• D. none of these

Answer 1

The correct option is B 1

Solution : Case I $x=3m\therefore 9m^2+3m+1\therefore$ not divisible by 3
Case II $x=3m+1\therefore 9m^2+9m+3\therefore$ divisible by 3
Case III $x=3m+2\therefore 9m^2+15m+7\therefore$ not divisible by 3
$\therefore$ If $x^2+x+1$ is divisible by 3, $x=3m+1$
$\therefore$ Remainder =1