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TIFR2010-Maths-B-15

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Which of the following statements is false?

  1. The polynomial $x^{2}+x+1$ is irreducible in $\mathbb{Z}/2\mathbb{Z}[x]$.
  2. The polynomial $x^{2}-2$ is irreducible in $\mathbb{Q}[x]$.
  3. The polynomial $x^{2}+1$ is reducible in $\mathbb{Z}/5\mathbb{Z}[x]$.
  4. The polynomial $x^{2}+1$ is reducible in $\mathbb{Z}/7\mathbb{Z}[x]$.
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