In each of the following two polynomials, find the value of `a` , if `x-a` is a factor: (i) `x^6-a x^5+x^4-a x^3+3x-a+2` (ii) `x^5-a^2x^3+2x+a+1`

Explanation

To solve the problem, we need to find the value of \( a \) such that \( x - a \) is a factor of the given polynomials. According to the Factor Theorem, if \( x - a \) is a factor of a polynomial \( P(x) \), then \( P(a) = 0 \).

### Part (i):
**Polynomial:** \( P(x) = x^6 - ax^5 + x^4 - ax^3 + 3x - a + 2 \)

1. **Substitute \( x = a \):**
\[
P(a) = a^6 - a \cdot a^5 + a^4 - a \cdot a^3 + 3a - a + 2 = 0
...