Identify the simplest polynomial function having integer coefficients with the given zeros: 3i,-1,2

Answer 1

For the given zeroes:

(x-3i)(x+1)(x-2)

To remove the imaginary component, multiply in the complex conjugate of (x-3i) since it didn't say that 3i,-1 and 2 were the only zeroes.

(x+3i)(x-3i)(x+1)(x-2)

Expanding

(x²+9)(x+1)(x-2)

(x³+x²+9x+9)(x-2)

x⁴+x³+9x²+9x -2x³-2x²-18x-18

x⁴-x³+7x²-9x-18