Answer:
[tex]f(x)=x^4-58x^2+1212x-10080[/tex]
Step-by-step explanation:
The given polynomial has zeros:
[tex]x=8,x=-14,x=3+9i[/tex]
By the complex conjugate property, [tex]x=3-9i[/tex] is also a zero of the polynomial.
The polynomial can be written in factored form as:
[tex]f(x)=(x-8)(x+14)(x-(3+9i))(x-(3-9i))[/tex]
We expand to get:
[tex]f(x)=(x^2+6x-112)(x^2-6x+90)[/tex]
We expand further to get:
[tex]f(x)=x^4-58x^2+1212x-10080[/tex]
The last choice is correct.
