Question

For any integer x, x squared -x will always produce an even value

Answer 1

Not at all:

The square of an even number will generate an even number and
The square of an odd number will generate an odd number

Answer 2

`(x^2 - x)` will always have an even value.

Explanation:

We are given an integer x.

Let x be even, then it can be written in the form x = 2n, where n is an integer.

If we evaluate,

`(x^2 - x) = (2n)^2 - 2n = 4n^2 - 2n = 2(2n^2 - n)`

Thus, it have an even value.

If we take x to be an odd integer, then,it can be written in the form x = 2n+1, where n is an integer.

`(x^2 - x) = (2n+1)^2 - 2n = 4n^2 + 2n = 2(2n^2 + n)`

Thus, it have an even value.

Thus,

`(x^2 - x)` will always have an even value.