Find the value of k, if `x-1`is a factor of `4x^3+3x^2-4x+k`.

Explanation

To find the value of \( k \) such that \( x - 1 \) is a factor of the polynomial \( 4x^3 + 3x^2 - 4x + k \), we can use the Remainder Theorem. Here’s the step-by-step solution:

### Step 1: Understand the Remainder Theorem
According to the Remainder Theorem, if \( x - c \) is a factor of a polynomial \( P(x) \), then \( P(c) = 0 \). In our case, since \( x - 1 \) is a factor, we will set \( c = 1 \).

### Step 2: Set up the polynomial
Let \( P(x) = 4x^3 + 3x^2 - 4x + k \).

...