Answer:
f(x) = [tex]x^{4} - 8x^{3} + 24x^{2} - 32x + 15[/tex]
Step-by-step explanation:
First of all, if 2 - i is a zero, then so is 2 + i
All you need to do now is multiply (x - 1)(x - 3)(x - 2 + i)(x - 2 - i)
I will do part of that multiplication
(x - 2 + i)(x - 2 - i) = [tex]x^{2}[/tex] - 2x - xi - 2x + 4 + 2i + xi - 2i - [tex]i^{2}[/tex]
= [tex]x^{2}[/tex] - 4x + 5
So, now (x - 1)(x - 3)([tex]x^{2}[/tex] - 4x + 5) = [tex]x^{4} - 8x^{3} + 24x^{2} - 32x + 15[/tex]
I will let you finish that multiplication. I did some and you can do some. OK?
