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 two given polynomials leave the same remainder when divided by \( (x-2) \).

### Step 1: Understand the Remainder Theorem
According to the Remainder Theorem, the remainder of a polynomial \( f(x) \) when divided by \( (x - c) \) is given by \( f(c) \). In this case, we will evaluate both polynomials at \( x = 2 \).

### Step 2: Evaluate the first polynomial at \( x = 2 \)
The first polynomial is:
\[
...