Given that 2 is a zero of the polynomial function $f(x)$, find the remaining zeros.
\[
f(x)=x^{3}-10 x^{2}+36 x-40
\]
List the remaining zeros (other than 2).
(Simplify your answer. Type an exact answer, using radicals and $i$ as needed. Use a comma to separate answers as needed.)
Answer
Final Answer: The remaining zeros of the polynomial function \(f(x) = x^{3} - 10x^{2} + 36x - 40\) are \(\boxed{4, 5}\).
Step 1 ：Given that 2 is a zero of the polynomial function \(f(x) = x^{3} - 10x^{2} + 36x - 40\), we can find the remaining zeros by dividing the polynomial by \((x - 2)\).
Step 2 ：The quotient polynomial is then \(x^{2} - 8x + 20\).
Step 3 ：We find the zeros of this polynomial by setting it equal to zero and solving for \(x\).
Step 4 ：Solving \(x^{2} - 8x + 20 = 0\) gives us the remaining zeros of the original polynomial.
Step 5 ：Final Answer: The remaining zeros of the polynomial function \(f(x) = x^{3} - 10x^{2} + 36x - 40\) are \(\boxed{4, 5}\).
