To ensure real coefficients, the complex conjugate of a complex zero must also be a zero. Therefore, the minimum set of zeros is
2 + i
2 - i
and the polynomial is
p(x) = A(x - 2) [x - (2 + i)] [x - (2 - i)],
where A ≠ 0.
A is the leading coefficient, so A = 1 (given).
p(x) = (x - 2) [x - (2 + i)] [x - (2 - i)]
Now multiply this through and simplify, and get your polynomial. The coefficients will all come out real.