Answer:
- (x - 2 + i)(x - 2 - i)(x - 1)
Step-by-step explanation:
In order to have rational polynomial, it has to have 2 + i as third zero.
Polynomial in factored form:
- (x - (2 - i))(x - (2 + i))(x - 1) =
- (x - 2 + i)(x - 2 - i)(x - 1)
Polynomial in standard form:
- (x^2 - 2x - ix - 2x + 4 +2i + ix - 2i -i^2)(x - 1) =
- (x^2 - 4x + 4 + 1)(x - 1) =
- (x^2 - 4x + 5)(x - 1) =
- x^3 - x^2 - 4x^2 + 4x + 5x - 5 =
- x^3 -5x^2 + 9x - 5
