Question

A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over .
3, −3 − 2i;    degree 3

Answer 1

a zero of 3 gives us a factor of (x-3)

complex zeros always come in conjugate pairs, so if
-3-2i is one of them, -3+2i must be another.
factors are (x - (-3-2i)) and (x - (-3+2i))
or (x + 3 + 2i) and (x + 3 - 2i)

multiply the last two to get a quadratic factor (......)

your f(x) = (x-3)(......)