Question Consider the function $f(x)=2 x^{4}-4 x^{3}+20 x-100$. What is the remainder if $f(x)$ is divided by $(x+11)$ ? Do not include the divisor Provide your answer below:

Step 1 ：Consider the function \(f(x)=2 x^{4}-4 x^{3}+20 x-100\).

Step 2 ：We are asked to find the remainder if \(f(x)\) is divided by \((x+11)\).

Step 3 ：According to the Remainder Theorem, if a polynomial \(f(x)\) is divided by \((x-a)\), the remainder is \(f(a)\).

Step 4 ：In this case, we are dividing by \((x+11)\), so we can find the remainder by evaluating \(f(-11)\).

Step 5 ：After evaluating, we find that the remainder is 34286.

Step 6 ：So, the remainder when \(f(x)\) is divided by \((x+11)\) is \(\boxed{34286}\).