question if $f(x) = x^6 - 4x - 4$, then what is the remainder when $f(x)$ is divided by $x - 1$?

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Accepted Answer

# Explanation:
## Step1: Recall the Remainder Theorem
The Remainder Theorem states that if a polynomial $ f(x) $ is divided by $ x - a $, the remainder is $ f(a) $. Here, we are dividing $ f(x) $ by $ x - 1 $, so $ a = 1 $.
## Step2: Evaluate $ f(1) $
Given $ f(x)=x^{6}-4x - 4 $, substitute $ x = 1 $ into the polynomial:
$$
\begin{align*}
f(1)&=(1)^{6}-4(1)-4\
&=1 - 4 - 4\
&=1-8\
&=- 7
\end{align*}
$$

# Answer:
The remainder is $-7$.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the Remainder Theorem

Step2: Evaluate \( f(1) \)

Answer: