If `x = 2` then the value of `x^(3) + 27x^(2) + 243x + 631` is

Options

A. 1233
B. 1211
C. 1231
D. 1321

Answer

To find the value of the expression \( x^3 + 27x^2 + 243x + 631 \) when \( x = 2 \), we will substitute \( x \) with 2 and calculate step by step.

### Step-by-step Solution:

1. **Substitute \( x = 2 \)**:
\[ x^3 + 27x^2 + 243x + 631 = 2^3 + 27(2^2) + 243(2) + 631 \]

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

3. **Calculate \( 27(2^2) \)**:
\[ 2^2 = 4 \quad \Rightarrow \quad 27 \times 4 = 108 \]

4. **Calculate \( 243(2) \)**:
\[ 243 \times 2 = 486 \]

5. **Now, combine all the calculated values**:
\[ 8 + 108 + 486 + 631 \]

6. **Add them step by step**:
- First, add \( 8 + 108 = 116 \)
- Next, add \( 116 + 486 = 602 \)
- Finally, add \( 602 + 631 = 1233 \)

Thus, the value of the expression when \( x = 2 \) is **1233**.

### Final Answer:
\[ \text{The value of } x^3 + 27x^2 + 243x + 631 \text{ when } x = 2 \text{ is } 1233. \]