If `x-2` is a factor of each of the following two polynomials, find the values of `a` in each case. (i) `x^3-2a x^2+a x-1` (ii) `x^5-3x^4-a x^3+3a x^2+2a x+4`

Explanation

To solve the problem step by step, we will find the value of \( a \) for each polynomial given that \( x - 2 \) is a factor.

### (i) For the polynomial \( x^3 - 2a x^2 + a x - 1 \):

1. **Identify the factor**: Since \( x - 2 \) is a factor, we know that substituting \( x = 2 \) into the polynomial should yield zero.

2. **Substitute \( x = 2 \)**:
\[
...