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Standard XI

Mathematics

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

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Solution

The correct option is A 1
Solution : Case I $x = 3 m ∴ 9 m^{2} + 3 m + 1 ∴$ not divisible by 3
Case II $x = 3 m + 1 ∴ 9 m^{2} + 9 m + 3 ∴$ divisible by 3
Case III $x = 3 m + 2 ∴ 9 m^{2} + 15 m + 7 ∴$ not divisible by 3
$∴$ If $x^{2} + x + 1$ is divisible by 3, $x = 3 m + 1$
$∴$ Remainder =1

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

The correct option is A 1Solution : 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