Write the polynomial $$ f(x) $$ that meets the given conditions. Answers may vary. Degree 3 polynomial with zeros of $$ -1,2 i $$, and $$ -2 i $$. $$ f(x)= $$

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We are given that the polynomial has zeros at  
$$
-1,\quad 2i,\quad -2i.
$$

**Step 1.** Write the factors corresponding to each zero.  
For zero $$ -1 $$: the factor is $$(x + 1)$$.  
For zeros $$ 2i $$ and $$ -2i $$: the factors are $$(x - 2i)$$ and $$(x + 2i)$$.

**Step 2.** Multiply the factors for the complex zeros.  
Notice that  
$$
(x - 2i)(x + 2i) = x^2 - (2i)^2.
$$
Since $$(2i)^2 = -4$$, we have  
$$
x^2 - (2i)^2 = x^2 - (-4) = x^2 + 4.
$$

**Step 3.** Write the polynomial as a product of the factors.  
Taking the polynomial to have a leading coefficient of $$1$$ (any nonzero constant would work), we have  
$$
f(x) = (x + 1)(x^2 + 4).
$$

**Step 4.** Optionally, expand the product.  
$$
f(x) = (x + 1)(x^2 + 4) = x(x^2 + 4) + 1(x^2 + 4) = x^3 + 4x + x^2 + 4.
$$
Reordering the terms gives  
$$
f(x) = x^3 + x^2 + 4x + 4.
$$

Thus, the polynomial is  
$$
\boxed{f(x) = (x + 1)(x^2 + 4) \quad \text{or} \quad f(x) = x^3 + x^2 + 4x + 4.}
$$
The polynomial is $$ f(x) = (x + 1)(x^2 + 4) $$ or $$ f(x) = x^3 + x^2 + 4x + 4 $$.

Write the polynomial \( f(x) \) that meets the given conditions. Answers may vary. Degree 3 polynomial with zeros of \( -1,2 i \), and \( -2 i \). \( f(x)= \)

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