If the polynomial `ax^(3)+3x^(2)-3` leaves the remainder 6 when divided by x-4, then find the value of a.

Explanation

To solve the problem, we need to find the value of \( a \) in the polynomial \( ax^3 + 3x^2 - 3 \) given that it leaves a remainder of 6 when divided by \( x - 4 \).

### Step-by-Step Solution:

1. **Understand the Remainder Theorem**:
According to the Remainder Theorem, if a polynomial \( P(x) \) is divided by \( x - c \), the remainder is \( P(c) \). In this case, we have \( c = 4 \).

2. **Set Up the Polynomial**:
...