For which values of `a` and `b`, the zeroes of `q(x) = x^(3)+2x^(2)+a` are also the zeroes of the polynomial `p(x) = x^(5)-x^(4)-4x^(3)+3x^(2)+3x +b`? Which zeores of `p(x)` are not the zeroes of `p(x)`?

Explanation

To solve the problem, we need to find the values of \( a \) and \( b \) such that the zeros of the polynomial \( q(x) = x^3 + 2x^2 + a \) are also the zeros of the polynomial \( p(x) = x^5 - x^4 - 4x^3 + 3x^2 + 3x + b \). We will also identify the zeros of \( p(x) \) that are not zeros of \( q(x) \).

### Step-by-Step Solution:

1. **Set Up the Division**:
We will divide \( p(x) \) by \( q(x) \) using polynomial long division. The goal is to find the remainder when \( p(x) \) is divided by \( q(x) \).

2. **Perform the Division**:
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