1 point Polynomial $Q$ has degree 3 and has zeros $-3,1+i$, and $1-i$. If $Q(x)=a x^{3}+b x^{2}+c x+d$, find $a, b, c$, and $d$.

Step 1 ：We are given a polynomial $Q$ of degree 3 with zeros $-3,1+i$, and $1-i$. The polynomial is in the form $Q(x)=a x^{3}+b x^{2}+c x+d$. We need to find the coefficients $a, b, c$, and $d$.

Step 2 ：We can express the polynomial $Q$ in terms of its zeros as $Q(x) = (x - (-3))(x - (1+i))(x - (1-i))$.

Step 3 ：Expanding this expression, we get $Q(x) = x^{3} + x^{2} - 4x + 6$.

Step 4 ：Comparing this with the general form $Q(x)=a x^{3}+b x^{2}+c x+d$, we can see that the coefficients are $a = 1, b = 1, c = -4, d = 6$.

Step 5 ：\(\boxed{a = 1, b = 1, c = -4, d = 6}\)