Subtract :
`x^(3) - 4x - 1` from `3x^(3) - x^(2) + 6`

Answer

To solve the problem of subtracting \( x^3 - 4x - 1 \) from \( 3x^3 - x^2 + 6 \), we can follow these steps:

### Step 1: Write the expression for subtraction
We need to subtract \( x^3 - 4x - 1 \) from \( 3x^3 - x^2 + 6 \). This can be expressed as:
\[ (3x^3 - x^2 + 6) - (x^3 - 4x - 1) \]

### Step 2: Distribute the negative sign
Next, we distribute the negative sign across the second expression:
\[ 3x^3 - x^2 + 6 - x^3 + 4x + 1 \]

### Step 3: Combine like terms
Now, we combine the like terms:
- For \( x^3 \): \( 3x^3 - x^3 = 2x^3 \)
- For \( x^2 \): There is only \(-x^2\), so it remains \(-x^2\)
- For \( x \): The term is \( 4x \)
- For the constant: \( 6 + 1 = 7 \)

Putting it all together, we have:
\[ 2x^3 - x^2 + 4x + 7 \]

### Final Answer
Thus, the result of subtracting \( x^3 - 4x - 1 \) from \( 3x^3 - x^2 + 6 \) is:
\[ \boxed{2x^3 - x^2 + 4x + 7} \]