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 \( P(x) = x^4 + x^3 + 8x^2 + ax + b \) is divisible by \( x^2 - 1 \), we can follow these steps:

### Step 1: Identify the roots of the divisor
The polynomial \( x^2 - 1 \) can be factored as \( (x - 1)(x + 1) \). Thus, the roots are \( x = 1 \) and \( x = -1 \).

### Step 2: Set up equations using the roots
Since \( P(x) \) is divisible by \( x^2 - 1 \), both \( P(1) \) and \( P(-1) \) must equal zero.

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