Find the value of k, if `x-1`is a factor of p(x) in each of the following cases:
(i) `p(x)=x^2+x+k` (ii) `p(x)=2x^2+k x+sqrt(2)`
(iii) `p(x)=k x^2-sqrt(2)x+1`(iv) `p(x)=k x^2-3x+k`

Explanation

To find the value of \( k \) such that \( x - 1 \) is a factor of \( p(x) \) in each of the cases provided, we will follow these steps for each polynomial.

### (i) \( p(x) = x^2 + x + k \)

1. **Set the divisor equal to zero**:
\[ x - 1 = 0 \implies x = 1 \]
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