Answer: The answer is \((n+\sqrt3i)(n-\sqrt3i)(n-1).\)
Step-by-step explanation: The given polynomial expression is
\(E=n^3-n^2+3n-3.\)
We are given to factor the above polynomial expression. Since the given polynomial is cubic, so there will be three factors.
The factorisation is as follows:
\(E\\=n^3-n^2+3n-3\\=n^2(n-1)+3(n-1)\\=(n^2+3)(n-1)\\=(n^2-3i^2)(n-1)\\=(n+\sqrt3i)(n-\sqrt3i)(n-1).\)
Thus, the factored polynomial is \((n+\sqrt3i)(n-\sqrt3i)(n-1).\)
