For what values of a ​​the function $y=x^6+ax^3-2x^3-2x^2+1$ is even I want to know for what valuyes this function is even
I know that $f(x)=f(-x)$ to proove that function is even. how its helps me?$$y=x^6+ax^3-2x^3-2x^2+1$$
Thanks!

$f(-x)=(-x)^6 + a(-x)^3 -2(-x)^3 -2(-x)^2 + 1 = x^6 -ax^3 + 2x^3 - 2x^2 +1 $
$= x^6 +(-a+2)x^3 -2x^2 +1$
So for the two polynomials to be equal we need $2-a=a-2$ Hence, $2a=4, a=2$
