That true. You have two ways to show it:
Method 1:
Factor the expression. You have
[tex] x^2-x = x(x-1) [/tex]
So, you're multiplying two consecutive numbers. One of them must be even, and if a factor of a product is even, the result will be even.
Method 2:
If x is even, [tex] x^2 [/tex] is even as well. So, [tex] x^2-x [/tex] is a subtraction between even numbers, which gives an even number.
If x is odd, [tex] x^2 [/tex] is odd as well. So, [tex] x^2-x [/tex] is a subtraction between odd numbers, which gives an even number.
A number is said to be an even number if it can be divided by 2, without leaving a remainder.
For any integer x, [tex]x^2 - x[/tex] will always be true.
Given that:
[tex]x \to integer[/tex]
[tex]x^2 - x[/tex] is represented as:
[tex]x^2 - x = x\times x - x[/tex]
Factor out x
[tex]x^2 - x = x(x - 1)[/tex]
Suppose x is even, x - 1 will be odd
Suppose x is odd, x - 1 will be even
This means that:
[tex]x^2 - x = Odd \times Even[/tex]
The product of an odd and an even number is even
So, we have:
[tex]x^2 - x = Even[/tex]
This means that: [tex]x^2 - x[/tex] will always be an even number
Read more about even and odd numbers at:
https://brainly.com/question/20243989
