Find the complex zeros of the following polynomial function. Write $f$ in factored form.
\[
f(x)=x^{3}-8 x^{2}+25 x-26
\]
Answer
The complex zeros of the polynomial function \(f(x)=x^{3}-8 x^{2}+25 x-26\) are \(\boxed{2}\), \(\boxed{3 - 2i}\), and \(\boxed{3 + 2i}\).
Step 1 ：Set the function equal to zero and solve for x to find the real zeros of the polynomial function.
Step 2 ：The real zeros of the polynomial are 2, 3 - 2i, and 3 + 2i.
Step 3 ：Since these zeros are already complex, there is no need to perform synthetic division and solve a quadratic equation.
Step 4 ：Therefore, the complex zeros of the polynomial are 2, 3 - 2i, and 3 + 2i.
Step 5 ：The complex zeros of the polynomial function \(f(x)=x^{3}-8 x^{2}+25 x-26\) are \(\boxed{2}\), \(\boxed{3 - 2i}\), and \(\boxed{3 + 2i}\).
