Find f(-3) given that
`f(x)=2x(x^2-8x+4)-3x^2-2`

Options

A. `-256`
B. 31
C. 193
D. -247

Answer

To find \( f(-3) \) given the function

\[ f(x) = 2x(x^2 - 8x + 4) - 3x^2 - 2, \]

we will substitute \( x = -3 \) into the function and simplify step by step.

### Step 1: Substitute \( x = -3 \)

We start by substituting \( -3 \) into the function:

\[ f(-3) = 2(-3)((-3)^2 - 8(-3) + 4) - 3(-3)^2 - 2. \]

### Step 2: Calculate \( (-3)^2 \)

Calculating \( (-3)^2 \):

\[ (-3)^2 = 9. \]

### Step 3: Substitute back into the equation

Now we substitute \( 9 \) back into the equation:

\[ f(-3) = 2(-3)(9 - 8(-3) + 4) - 3(9) - 2. \]

### Step 4: Calculate \( -8(-3) \)

Calculating \( -8(-3) \):

\[ -8(-3) = 24. \]

### Step 5: Substitute back into the equation

Now substitute \( 24 \) back into the equation:

\[ f(-3) = 2(-3)(9 + 24 + 4) - 27 - 2. \]

### Step 6: Simplify inside the parentheses

Now simplify \( 9 + 24 + 4 \):

\[ 9 + 24 + 4 = 37. \]

### Step 7: Substitute back into the equation

Substituting \( 37 \) back into the equation gives:

\[ f(-3) = 2(-3)(37) - 27 - 2. \]

### Step 8: Calculate \( 2(-3)(37) \)

Calculating \( 2(-3)(37) \):

\[ 2(-3)(37) = -222. \]

### Step 9: Substitute back into the equation

Now substitute \( -222 \) back into the equation:

\[ f(-3) = -222 - 27 - 2. \]

### Step 10: Combine the terms

Now combine the terms:

\[ -222 - 27 = -249, \]
\[ -249 - 2 = -251. \]

### Final Answer

Thus,

\[ f(-3) = -251. \]