Using polynomial long division, we see that

How can we factor ? Such a polynomial is called **bi-quadratic**. It can be solved by the following trick: we substitute to obtain

By the guessing method, we see that its factorization is given by:

Thus the roots are *y*=-1 and *y*=-2. But from this we can calculate the roots in terms of *x*; recall that .
Consequently the roots of the bi-quadratic polynomial are all complex: and .

Over the complex numbers, we can factor the polynomial as

Over the real numbers, the polynomials and are irreducible. Thus the polynomial's factorization is:

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Tue Jun 24 12:46:21 MDT 1997

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