Prove constraint relationship

Use given constraints to derive a formula for a quantity in terms of a single variable.

1 questions · Moderate -0.3

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SPS SPS SM 2025 February Q4
6 marks Moderate -0.3
  1. The number \(K\) is defined by \(K = n^3 + 1\), where \(n\) is an integer greater than \(2\). Given that \(n^3 + 1 = (n + 1) (n^2 + bn + c)\), find the constants \(b\) and \(c\). [1]
  2. Prove that \(K\) has at least two distinct factors other than \(1\) and \(K\). [5]