Is the function f(x) = x^4 - 3x² + 5 even, odd, or neither?

A function is even when $f(-x)=f(x)$ for every $x$, and odd when $f(-x)=-f(x)$. Here $f(-x)=(-x)^4-3(-x)^2+5=x^4-3x^2+5=f(x)$, because even powers erase the negative sign. So $f$ is even, choice A. Choice B (odd) would need $f(-x)=-f(x)$, which fails: for example, $f(1)=3$ but $f(-1)=3$, not $-3$. Choice C (neither) would be correct only if the symmetry broke somewhere, for example if there were an odd power like $x^3$. Choice D is wrong because the test above settles the question completely.