Factor $x^4-7x^2+1$ Is there a general method of factoring fourth order polynomials into a product of two irreducible quadratics? 
As I am reviewing on finding roots of polynomials in $\mathbb Z_n$ for abstract algebra, I am trying to factor the polynomial $x^4-7x^2+1$, and I was given the answer of $(x^2+3x+1)(x^2-3x+1)$. 
I was able to verify this of course by multiplying together the two irreducible quadratics, but I need to pretend that I never received the answer in the first place and ask for any hint in proceeding how to factor the fourth-order polynomial. Thanks.
It feels like I should use a method of "difference of squares" more than anything...

Hint:
Try with $$(x^2\pm1)^2-*x^2$$
The coefficient of $x^2$  has to be perfect square
