If the polynomials `ax^3+4x^2+3x-4` and `x^3-4x+a` leave the same remainder when divided by `(x-3),` find the value of `a`

Explanation

To find the value of \( a \) such that the polynomials \( ax^3 + 4x^2 + 3x - 4 \) and \( x^3 - 4x + a \) leave the same remainder when divided by \( (x - 3) \), we can follow these steps:

### Step 1: Understand the Remainder Theorem
According to the Remainder Theorem, when a polynomial \( f(x) \) is divided by \( (x - c) \), the remainder is \( f(c) \). In this case, we will evaluate both polynomials at \( x = 3 \).

### Step 2: Evaluate the First Polynomial at \( x = 3 \)
Let \( f(x) = ax^3 + 4x^2 + 3x - 4 \).

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