Answer:
Standard form: 
Factored form with complex numbers: 
Factored form without complex numbers: 
Step-by-step explanation:
If the polynomial has real coefficients and a+bi is a zero, then a-bi zero.
This means the following:
1) Since 3+i is a zero, then 3-i is a zero.
2) Since 3-2i is a zero, then 3+2i is a zero.
So we have the following zeros:
1) x=2
2) x=3+i
3) x=3-i
4) x=3-2i
5) x=3+2i
If x=c is a zero of the polynomial, then x-c is a factor of the polynomial.
This implies the following:
1) x=2 is a zero => x-2 is a factor
2) x=3+i is a zero => x-(3+i) is a factor
3) x=3-i is a zero => x-(3-i) is a factor
4) x=3-2i is a zero => x-(3-2i) is a factor
5) x=3+2i is a zero => x-(3+2i) is a factor
Let's put our factors together:

Let's find the standard form for this polynomial.
This will require us to multiply the above out and simplify by combining any like terms.
Before we begin this process, I would rather have a quick way to multiply the factors that contain the congregate pair zeros.

I'm going to use foil.
First: 
Outer: 
Inner: 
Last: 
(Note:
; When multiplying conjugates, you just have to multiply the first terms of each and the last terms of each.)
------------------------------------Let's combine these terms:

Distribute:

Combine like terms:

So the formula we will be using on the factors that contain conjugate pair zeros is:
.






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So this is what we have now:

I'm going to multiply the last two factors:

What we are going to do is multiply the first term in the first ( ) to every term in the second ( ).
We are also going to do the same for the second term in the first ( ).
Then the third term in the first ( ).









--------------------------------Combine like terms:

-----------------------------------------------------------------
So now we have

We are almost done.
We are going to multiply the first term in the first ( ) to every term in the second ( ).
We are going to multiply the second term in the first ( ) to every term in the second ( ).










----------------------------------------Combine like terms:
