If x = -2, find the value of `3x^(3)– 5x^(2) +4`.

Answer

To find the value of the expression \(3x^3 - 5x^2 + 4\) when \(x = -2\), we will follow these steps:

### Step 1: Substitute the value of \(x\)
We start by substituting \(x = -2\) into the expression:
\[ 3(-2)^3 - 5(-2)^2 + 4 \]

### Step 2: Calculate \((-2)^3\)
Next, we calculate \((-2)^3\):
\[ (-2)^3 = -2 \times -2 \times -2 = -8 \]
So, we can rewrite the expression as:
\[ 3(-8) - 5(-2)^2 + 4 \]

### Step 3: Calculate \((-2)^2\)
Now, we calculate \((-2)^2\):
\[ (-2)^2 = -2 \times -2 = 4 \]
Now, substitute this back into the expression:
\[ 3(-8) - 5(4) + 4 \]

### Step 4: Multiply the coefficients
Now we multiply the coefficients:
\[ 3 \times -8 = -24 \]
\[ -5 \times 4 = -20 \]
So, the expression now looks like:
\[ -24 - 20 + 4 \]

### Step 5: Combine the terms
Now, we combine the terms:
\[ -24 - 20 = -44 \]
Then add 4:
\[ -44 + 4 = -40 \]

### Final Answer
Thus, the value of the expression \(3x^3 - 5x^2 + 4\) when \(x = -2\) is:
\[ \boxed{-40} \]

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