For what value of `K, (x - 1)` is a factor of `(x^3-K)`.

Options

A. `-1`
B. 1
C. 8
D. `-8`

Answer

To find the value of \( K \) for which \( (x - 1) \) is a factor of \( (x^3 - K) \), we can follow these steps:

### Step 1: Set up the equation
Since \( (x - 1) \) is a factor of \( (x^3 - K) \), we know that if we substitute \( x = 1 \) into the polynomial \( (x^3 - K) \), the result should be zero.

### Step 2: Substitute \( x = 1 \)
Substituting \( x = 1 \) into the polynomial gives us:
\[ (1)^3 - K = 0 \]

### Step 3: Simplify the equation
This simplifies to:
\[ 1 - K = 0 \]

### Step 4: Solve for \( K \)
To find \( K \), we can rearrange the equation:
\[ K = 1 \]

### Conclusion
Thus, the value of \( K \) for which \( (x - 1) \) is a factor of \( (x^3 - K) \) is:
\[ \boxed{1} \]

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