If you simplify $x^{3} - 3 x^{2} + 3 x + 7$ its factors are

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Solution

$x^{3} - 3 x^{2} + 3 x + 7 = x^{3} - 3 x^{2} + 3 x - 1 + 8 = (x - 1)^{3} - 2^{3} = (x - 1 - 2) ((x - 1)^{2} + 4) = (x - 3) (x^{2} - 2 x + 5)$
The factors of $x^{3} - 3 x^{2} + 3 x + 7$ are $x - 3, x^{2} - 2 x + 5$

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