Find the value of 'a', if (x - a) is a factor of `x^(3)-ax^2+x+2`.

Answer

To find the value of 'a' such that \( (x - a) \) is a factor of the polynomial \( P(x) = x^3 - ax^2 + x + 2 \), we can follow these steps:

### Step 1: Set Up the Polynomial
Let \( P(x) = x^3 - ax^2 + x + 2 \).

### Step 2: Use the Factor Theorem
According to the Factor Theorem, if \( (x - a) \) is a factor of \( P(x) \), then \( P(a) = 0 \).

### Step 3: Substitute \( x = a \) into the Polynomial
Now, we will substitute \( x = a \) into the polynomial:
\[ P(a) = a^3 - a \cdot a^2 + a + 2 \]

### Step 4: Simplify the Expression
Simplifying the expression:
\[ P(a) = a^3 - a^3 + a + 2 \]
The \( a^3 \) terms cancel out:
\[ P(a) = a + 2 \]

### Step 5: Set the Polynomial Equal to Zero
Since \( P(a) = 0 \):
\[ a + 2 = 0 \]

### Step 6: Solve for 'a'
Now, solve for \( a \):
\[ a = -2 \]

### Conclusion
Thus, the value of \( a \) is \( -2 \).

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