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:

Answer

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Answer

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

Steps

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 $\boxed{34286}$.