use the complex zeros to give fully factored form, the first factor needs a x in it : (-3) (-2i)(x+2i)
It appears you want (x-3)(x-2i)(x+2i)
Once again you have a garbled question. Either name the roots or the factors. You have a mix of both.
The question is how you go from x^2+4, to -2i.
To find the fully factored form of the polynomial using the complex zeros, you can follow these steps:
Step 1: Identify the complex zeros. In this case, the given complex zeros are -2i and 2i.
Step 2: Use the complex conjugate property. Since complex zeros occur in conjugate pairs, you know that if -2i is a zero, then its conjugate 2i must also be a zero.
Step 3: Set up the factors. Based on the zeros, the factors can be represented as follows:
(x - (-3))(x - (-2i))(x - 2i)
Step 4: Simplify the factors. Remove the double negative signs and combine like terms:
(x + 3)(x + 2i)(x - 2i)
Step 5: Rearrange the factors. In the given form, it is specified that the first factor should include an x. So, we can rearrange the factors accordingly:
(x + 3)(x - 2i)(x + 2i)
Thus, the polynomial, represented in the fully factored form with the first factor containing an x, is (x + 3)(x - 2i)(x + 2i).