Question

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

Third-degree, with zeros of 3−i, 3+i, and 2, and a leading coefficient of −3.

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`