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 `q(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 determine which zeros of \( p(x) \) are not zeros of \( q(x) \).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
Since the zeros of \( q(x) \) are also zeros of \( p(x) \), it implies that \( q(x) \) is a factor of \( p(x) \). Therefore, when we divide \( p(x) \) by \( q(x) \), the remainder should be zero.

2. **Perform Polynomial Long Division**:
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