Question

How do I factor out an equation with zeros of : 2 (multiplicity of 2), 1 + 2i, 1-2i

Answer 1

(x - 2)^2(x - (1 + 2i))(x - (1 - 2i))
(x - 2)(x - 2)(x - 1 - 2i)(x - 1 + 2i)
(x^2 - 4x + 4)(x^2 - x + 2ix - x + 1 - 2i - 2ix + 2i + 4)
(x^2 - 4x + 4)(x^2-2x + 5)
x^4 - 2x^3 + 5x^2 - 4x^3 + 8x^2 - 20x + 4x^2 - 8x + 20
x^4 - 6x^3 + 9x^2 - 28x + 20