If `A = 4x^(3) -8x^(2), B = 7x^(3) -5x + 3 and C = 3x^(3) + x - 11`, then find `2A -3B + 4C`

Answer

To find \(2A - 3B + 4C\), we will first calculate \(2A\), \(3B\), and \(4C\) separately and then combine them.

### Step 1: Calculate \(2A\)
Given:
\[ A = 4x^3 - 8x^2 \]

Now, calculate \(2A\):
\[ 2A = 2 \times (4x^3 - 8x^2) = 8x^3 - 16x^2 \]

### Step 2: Calculate \(3B\)
Given:
\[ B = 7x^3 - 5x + 3 \]

Now, calculate \(3B\):
\[ 3B = 3 \times (7x^3 - 5x + 3) = 21x^3 - 15x + 9 \]

### Step 3: Calculate \(4C\)
Given:
\[ C = 3x^3 + x - 11 \]

Now, calculate \(4C\):
\[ 4C = 4 \times (3x^3 + x - 11) = 12x^3 + 4x - 44 \]

### Step 4: Combine \(2A\), \(-3B\), and \(4C\)
Now we need to calculate \(2A - 3B + 4C\):
\[ 2A - 3B + 4C = (8x^3 - 16x^2) - (21x^3 - 15x + 9) + (12x^3 + 4x - 44) \]

### Step 5: Simplify the expression
First, distribute the negative sign:
\[ = 8x^3 - 16x^2 - 21x^3 + 15x - 9 + 12x^3 + 4x - 44 \]

Now, combine like terms:
1. For \(x^3\):
\[ 8x^3 - 21x^3 + 12x^3 = (8 - 21 + 12)x^3 = -1x^3 \]
2. For \(x^2\):
\[ -16x^2 = -16x^2 \]
3. For \(x\):
\[ 15x + 4x = 19x \]
4. For the constant terms:
\[ -9 - 44 = -53 \]

Putting it all together, we have:
\[ 2A - 3B + 4C = -x^3 - 16x^2 + 19x - 53 \]

### Final Result
Thus, the final expression is:
\[ \boxed{-x^3 - 16x^2 + 19x - 53} \]