SOLUTION: How to factor8x^4-14x^2+3

1.  Introduce new variable  u = .
    Then the polynomial takes the form  .

2.  Find the roots of the polynomial  .

    For it, solve the quadratic equation   = .

    Use the quadratic formula. You will get 

     =  = .

    So,   =   and   = .


3.  Hence, the quadratic polynomial    is

     =  = (2u-3)*(4u-1).

    Correspondingly,  the  original polynomial factorization is 

     = .


4.  Next, you can factor further each of the two factors above to get

     = .


It is what you were asking for.

 ------- Replacing 





 ------- Factoring  further