Question

How do you determine if `p( x) = -(x-4)(x-2)(x+4)(x+2)` is an even or odd function?

Answer 1

`p(x)` is even.

Explanation:

To identify whether a function `f(x)` is odd or even find out `f(-x)`. If `f(-x)=f(x)`, the function is even and if `f(-x)=-f(x)`, the function is odd.

Here, as `p(x)=-(x-4)(x-2)(x+4)(x+2)`

`p(-x)=-(-x-4)(-x-2)(-x+4)(-x+2)`

= `-(-(x+4))(-(x+2))(-(x-4))(-(x-2))`

= `-(x+4)((x+2)(x-4)(x-2)`

or `p(-x)=-(x-4)(x-2)(x+4)(x+2)=p(x)`

Hence, `p(x)` is even.