Find a polynomial with integer coefficients that satisfies the given conditions. \( Q(x)=\square \) has degree 3 and zeros -9 and \( 1+i \).

To construct a polynomial \( Q(x) \) with integer coefficients of degree 3, we start by noting the zeros given: \(-9\) and \(1+i\). Since polynomial coefficients must be integers, the conjugate of \(1+i\), which is \(1-i\), must also be a zero. We can therefore express the polynomial as: \[ Q(x) = (x + 9)(x - (1+i))(x - (1-i)). \] Next, we simplify the complex factors: \[ (x - (1+i))(x - (1-i)) = (x - 1 - i)(x - 1 + i) = (x - 1)^2 + 1^2 = (x - 1)^2 + 1 = x^2 - 2x + 1 + 1 = x^2 - 2x + 2. \] Now our polynomial can be written as: \[ Q(x) = (x + 9)(x^2 - 2x + 2). \] Expanding this gives: \[ Q(x) = x^3 - 2x^2 + 2x + 9x^2 - 18x + 18 = x^3 + 7x^2 - 16x + 18. \] Thus, the polynomial with integer coefficients that meets these requirements is: \[ Q(x) = x^3 + 7x^2 - 16x + 18. \]