If x-1 is a factor of `x^2+ax-4` , then a has the value

Options

A. 4
B. 3
C. 2
D. 1

Explanation

To solve the problem step by step, we will use the fact that if \( x - 1 \) is a factor of the polynomial \( x^2 + ax - 4 \), then substituting \( x = 1 \) into the polynomial should yield zero.

### Step-by-Step Solution:

1. **Identify the Factor**: Since \( x - 1 \) is a factor, we can set \( x - 1 = 0 \) which gives us \( x = 1 \).

2. **Substitute into the Polynomial**: Substitute \( x = 1 \) into the polynomial \( x^2 + ax - 4 \):
\[ 1^2 + a(1) - 4 = 0 \]

3. **Simplify the Equation**: This simplifies to:
\[ 1 + a - 4 = 0 \]

4. **Combine Like Terms**: Combine the constants:
\[ a - 3 = 0 \]

5. **Solve for \( a \)**: Rearranging gives:
\[ a = 3 \]

Thus, the value of \( a \) is \( 3 \).

### Final Answer:
The value of \( a \) is \( 3 \).

---