If `x = 2 ` then the value of ` x^(3) + 27 x^(2) + 243 x + 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 can substitute \( x \) with 2 and calculate step by step.

### Step-by-Step Solution:

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

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

3. **Calculate \( 27(2^2) \)**:
\[ 2^2 = 4 \quad \text{so} \quad 27(2^2) = 27 \times 4 = 108 \]

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

5. **Now, substitute these values back into the expression**:
\[ 8 + 108 + 486 + 631 \]

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

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