Factor n 3 - n 2 + 3n - 3.

Mathematics

2 answers:

son4ous [18]3 years ago

7 0

N³- n² + 3n - 3 = (n²+3 )(x-1 )

Leokris [45]3 years ago

6 0

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 $(n+\sqrt3i)(n-\sqrt3i)(n-1).$

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