Question

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

Answer 1

If you want a polynomial with zeroes $x_1,x_2,x_3$ and lead coefficient $a$ you simply have to multiply

$a(x-x_1)(x-x_2)(x-x_3)$

So, in this case, we have

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

If we multiply all the pieces, we have

$-3 x^3 + 24 x^2 - 66 x + 60$