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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