Question 927066
<pre>
Since the coeffcients are real, and 3+i is a solution, so is its
conjugate 3-i

Start with 

      x=-2,  x=4,     x=3+i,    x=3-i
    x+2=0, x-4=0, x-3-i=0   x-3+i=0 

Multiply all the left sides and all the right sides, which gives

  (x+2)(x-4)(x-3-i)(x-3+i) = 0

Do all that multiplying remembering that i<sup>2</sup> = -1

and get

        x<sup>4</sup>-8x<sup>3</sup>+14x<sup>2</sup>+28x-80 = 0

So the polynomial function f(x) is

 f(x) = x<sup>4</sup>-8x<sup>3</sup>+14x<sup>2</sup>+28x-80 

Edwin</pre>