Find the value of `a ,` if `x-a` is a factor of `x^3-a^2x+x+2`

Explanation

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

### Step 1: Use the Factor Theorem
According to the Factor Theorem, if \( x - a \) is a factor of a polynomial \( P(x) \), then \( P(a) = 0 \).

### Step 2: Substitute \( x = a \) into the polynomial
We substitute \( x = a \) into the polynomial \( P(x) = x^3 - a^2x + x + 2 \):
\[
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