BY actual division , find the quotient and the remainder when the first polynomial is divided by the second polynomial `x^(4)+1 and x-1` .

Explanation

To find the quotient and the remainder when the polynomial \( x^4 + 1 \) is divided by \( x - 1 \) using actual division, we will follow these steps:

### Step 1: Set Up the Division
We will set up the polynomial long division by writing \( x^4 + 1 \) (the dividend) under the long division symbol and \( x - 1 \) (the divisor) outside.

\[
\begin{array}{r|l}
x - 1 & x^4 + 0x^3 + 0x^2 + 0x + 1 \\
...