Find the value of the expression for the given value of x.
`x^(3)+7x^(2)+8x-1`, when `x= -2`.

Answer

To find the value of the expression \( x^3 + 7x^2 + 8x - 1 \) when \( x = -2 \), we will substitute \(-2\) into the expression and simplify step by step.

### Step-by-Step Solution:

1. **Write the expression with the value of x substituted:**
\[ (-2)^3 + 7(-2)^2 + 8(-2) - 1 \]

2. **Calculate \((-2)^3\):**
\[ (-2)^3 = -2 \times -2 \times -2 = -8 \]

3. **Calculate \(7(-2)^2\):**
\[ (-2)^2 = 4 \quad \text{(since multiplying two negative numbers gives a positive)} \]
\[ 7 \times 4 = 28 \]

4. **Calculate \(8(-2)\):**
\[ 8 \times -2 = -16 \]

5. **Now substitute these values back into the expression:**
\[ -8 + 28 - 16 - 1 \]

6. **Combine the terms step by step:**
- First, combine \(-8\) and \(28\):
\[ -8 + 28 = 20 \]
- Next, combine \(20\) and \(-16\):
\[ 20 - 16 = 4 \]
- Finally, combine \(4\) and \(-1\):
\[ 4 - 1 = 3 \]

7. **Final result:**
\[ \text{The value of the expression when } x = -2 \text{ is } 3. \]