If the polynomials `az^3+4z^2+3z-4` and `z^3-4z+a` leave the same remainder when divided by `z-3` , find the value of a.

Explanation

To solve the problem, we need to find the value of \( a \) such that the polynomials \( p_1(z) = az^3 + 4z^2 + 3z - 4 \) and \( p_2(z) = z^3 - 4z + a \) leave the same remainder when divided by \( z - 3 \).

### Step 1: Use the Remainder Theorem
According to the Remainder Theorem, the remainder of a polynomial \( p(z) \) when divided by \( z - c \) is \( p(c) \). Here, we will evaluate both polynomials at \( z = 3 \).

### Step 2: Evaluate \( p_1(3) \)
Substituting \( z = 3 \) into \( p_1(z) \):
\[
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