Find the values of a and b so that `x^4+x^3+8x^2+a x+b` is divisible by `x^2+1.`

Explanation

To find the values of \( a \) and \( b \) such that the polynomial \( x^4 + x^3 + 8x^2 + ax + b \) is divisible by \( x^2 + 1 \), we will use polynomial long division and ensure that the remainder is zero.

### Step-by-Step Solution:

1. **Set Up the Division**: We want to divide \( x^4 + x^3 + 8x^2 + ax + b \) by \( x^2 + 1 \).

2. **First Division Step**:
- Divide the leading term \( x^4 \) by \( x^2 \) to get \( x^2 \).
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