Answer
$f(x)=2x^{3}-2x^{2}+50x-50$
Work Step by Step
The Linear Factorization Theorem...
An nth-degree polynomial can be expressed as the product of a nonzero constant and $n$ linear factors, where each linear factor has a leading coefficient of 1.
Imaginary roots, if they exist, occur in conjugate pairs.
-------------------------
If $5i$ is a zero, so is $-5i.$
$f(x)=a_{n}(x-1)(x+5i)(x-5i)$
$f(x)=a_{n}(x-1)(x^{2}+25)$
Using the given $f(-1),$we find $a_{n}:$
$f(-1)=a_{n}(-1-1)(1+25)$
$-104=a_{n}(-52)$
$a_{n}=2$
so,
$f(x)=2(x-1)(x^{2}+25)$
$f(x)=2(x^{3}+25x-x^{2}-25)$
$f(x)=2(x^{3}-x^{2}+25x-25)$
$f(x)=2x^{3}-2x^{2}+50x-50$
