If the polynomials `a x^3+3x^2-13` and `2x^3-5x+a ,` when divided by `(x-2)` leave the same remainder, find the value of `a` .

Explanation

To solve the problem, we need to find the value of \( a \) such that the polynomials \( p(x) = ax^3 + 3x^2 - 13 \) and \( q(x) = 2x^3 - 5x + a \) leave the same remainder when divided by \( (x - 2) \).

### Step-by-Step Solution:

1. **Understanding Remainders**:
When a polynomial \( f(x) \) is divided by \( (x - c) \), the remainder is given by \( f(c) \). Here, we will evaluate both polynomials at \( x = 2 \).

2. **Evaluate \( p(2) \)**:
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