What will be the value of
`n ^(4) -10 n ^(3) + 36 n ^(2) - 49 n + 24` if n =1 ?

Options

A. 21
B. 2
C. 1
D. 22

Answer

To find the value of the expression \( n^4 - 10n^3 + 36n^2 - 49n + 24 \) when \( n = 1 \), we will substitute \( n \) with 1 and simplify step by step.

### Step-by-Step Solution:

1. **Substitute \( n = 1 \) into the expression:**
\[ 1^4 - 10 \cdot 1^3 + 36 \cdot 1^2 - 49 \cdot 1 + 24 \]

2. **Calculate each term:**
- \( 1^4 = 1 \)
- \( 10 \cdot 1^3 = 10 \)
- \( 36 \cdot 1^2 = 36 \)
- \( 49 \cdot 1 = 49 \)

Now substituting these values back into the expression gives:
\[ 1 - 10 + 36 - 49 + 24 \]

3. **Combine the terms:**
- Start with \( 1 - 10 = -9 \)
- Then add \( 36 \):
\[ -9 + 36 = 27 \]
- Next, subtract \( 49 \):
\[ 27 - 49 = -22 \]
- Finally, add \( 24 \):
\[ -22 + 24 = 2 \]

4. **Final result:**
The value of the expression when \( n = 1 \) is:
\[ \boxed{2} \]