factor fully

f(x) = x^4 - 5x^2 + 4

Let u=x^{2}

Then, we get u^{2}-5u+4

Now, factor the quadratic and resub.

u^{2}-5u+4=(u-4)(u-1)

Since u=x^{2}, resub:

(x^{2}-4)(x^{2}-1)

Note the difference of two squares in both.

(x+2)(x-2)(x+1)(x-1)